So, to get a sport into the Olympics it has to have an International Federation that the IOC can deal with. For Cycling that's the Union Cycliste Internationale, for Shooting it's the International Shooting Sports Federation.
The IOC will only really deal with one federation per sport - so UCI set the rules as used at the Olympics for road and track (velodrome) cycling as well as BMX and mountain biking despite them all being quite different disciplines, and similarly they would look to the ISSF for all guidance on shooting events.
So that's the first hurdle - the IPSC would have to merge into the ISSF. Aside from beating through the politics, there are substantial financial implications. World Cups for instance come in 3 flavours - Shotgun; Rifle and Pistol; All three.
So all the sites currently used for Rifle and Pistol World Cups, etc are going to need IPSC type ranges constructing on them, and funding will have to be found to run those extra events, or you farm of Practical Disciplines into a separate group - Shotgun; Rifle and Pistol; Practical - so they have their own world cups at suitable venues. But that's a bit weird. Try and explain why Running Deer should stay with "Range Rifle" rather than being "Practical". Either way there needs to be a lot of investment in facilities.
Then, you would have to convince the IOC that they needed extra shooting events - there are several ISSF events that are contested at World Cup level but not featured at the Olympics - 300metre Rifle, Running Deer and Standing Boar for example. The ranges required are incompatible with the other rifle and pistol disciplines (which can all share a fairly multi-purpose range layout), and so it's a lot of extra expense and construction effort for a single additional discipline. More to the point, a lot of extra expense for disciplines which overall don't bring in as much media attention and sponsorship revenue as others.
There are also some events which are not universal - for instance in Olympic Rifle, the Men have Prone, 3-Position and Air. Women have no Prone event, just Air and 3P. Similarly there is no Women's 50metre Free Pistol event. They have Air and Sport Pistol events, whilst men have Air, Rapid Fire and Free Pistol.
So if you once merged IPSC into ISSF and got the IPSC type events at the World Cups and Championships along side the other rifle and pistol events, you're going to have to justify why practical disciplines should be put forward to the Olympics instead of say, Running Deer, because there's a whole bunch of other disciplines that also have a fair shout for inclusion.
That said, IPSC type disciplines would probably provide a much better spectator event than the current events. The ISSF have spent a heck of a lot of time trying to make it more media friendly, but fundamentally the rifle and pistol stuff is still people on a firing point shooting at a target you can't see (although they use electronic targets now so spectators can at least see the fall of shot on big screens). It's not compulsive viewing though. The clays are a bit better, with moving targets, puffs of orange dust and shorter details.
All that was quite negative, and it's certainly not to say it can't be done, but I've been on a lot of sports forums and heard "We should have such and such in the Olympics", and it's not as simple as just petitioning the IOC to let you in. You need a federation, which can get political if you're overlapping with other areas of the same sport. Then you've got to make the business case, because either someone has to spend money and build range facilities for your event, or you're going to be kicking another sport out the way to make room for you, and you have to explain why your competitors are more worthy than that other sport's competitors.
The Biathlon I quite enjoy watching, but then I enjoy watching skiing anyway, and depending on the coverage, they can also put overlays of the targets up so as the skiers hit the firing line you can see their hits/misses and whether they're getting time penalties. I also view it as a very pure sport - it's pretty much identical to what you would do if you were either hunting or fighting a running skirmish. Sure the rifles are a bit more specialised and they wear lycra, but then depending on whether you were hunting or fighting you'd likely be using a different rifle and probably wearing different clothes, so I don't see the issue there. Understandably they have a massive following in Scandinavia, which is pretty much where the discipline originated from, as part of people's way of life.
All "smalltime" sports are being marginalized, and by "smalltime" I mean that sport doesn't get TV ratings or generate other big buzz here in the USA. Even chartered sports (a chartered Olympic sport is a sport that is required to appear in every Olympics, as opposed to say an exhibition sport, which varies at the discretion of the host nation) are feeling the pressure from Dick Ebersol (now Mike Lazarus) and his band of greedy corporate goons. He has slashed funding tremendously to small sports (remember: the USA is the only country on Earth where the athletes get zero government money, as it should be, but therefore if we don't get money from the Olympic committee, it means we're on our own against essentially pros from other countries) in order to throw more money at sports that his focus groups suggest will sell well with advertisers -- that's how we end up with abominations like ballroom dancing, rhythmic gymnastics and golf.
From a former athlete's perspective, I don't want most shooting sports in the Games. Most athletes in the Games that I've known over the years feel this way:
1) Are your top competitors some of the best athletes in the world?
2) Does your sport have an objective score?
If you answer yes to both questions, most athletes I've known would want that sport to be part of the Games. Shooting is a big "no" to the first question. Same with golf.
Ballroom dancing, gymnastics, etc fail the second question, and many of us don't consider them sports even though there are some quality athletes. We call them "beauty contests" because a judge has to tell you if you've won or not, which in the opinion of many, sucks.
Sorry for the long rant
What you've mentioned there is actually one of the reasons I want to see shooting at the Olympics. It's a small sport and doesn't attract huge ad dollars. The five rings are often the only attraction to advertisers and funding bodies. ISSF shooting isn't a big spectator sport and we can't do full IPSC in the UK - not properly, on account of not having proper pistols, so we'd be screwed if that was the Olympic discipline! And it sounds like the Netherlands may be having issues with IPSC type shooting.
You mentioned golf - golf doesn't need the Olympics (not that it's featured anyway, even if it is recognised), just life Soccer, Tennis and Rugby. The Olympics is not the pinnacle for any of those sports. As a soccer player, winning the Olympics is nice and all, but you really want the World Cup. Same in Tennis - Wimbledon's the one to win, and Golf has the Masters.
I cans see what you're getting at with your two criteria, but from a grassroots level, I also view "Sports" as being a demonstration and competition of some useful real-world skill. I would tag that in as a third criteria. If we consider the original Ancient Olympics, it was basically track and field, and much of it combat-derived at that. People demonstrating their prowess or strength. I would certainly count archery in, even if it's competitors are not strictly athletes. And shooting and fencing then follow the same line, and possibly gymnastics - but certainly not rhythmic gymnastics. And open-water swimming, but not synchronised diving or synchronised swimming. They can take a running jump (and do, frequently

)
But what about Games? Football and Tennis require athleticism, but they serve no useful purpose in the real world, they are just games designed to foster teamwork and hand-eye co-ordination respectively.
My view is you might as well toss Football and Tennis out - it's neither the pinnacle of their sport, nor a stepping stone to it, so what are they doing there? And what Rugby Sevens is doing being trialled this year I don't know. There's another big-ad revenue game that doesn't need the Olympics. The Football is basically a juniors event, and competing in Tennis is subject to not having a more important (profitable) event to attend! Same goes for Road Cycling and BMX - surely the Tour de France and X-Games are the ones to win? Obviously BMX's inclusion is ad-revenue driven.
For shooting, the Olympics is the big one. It's what the World Cups and Championships lead to. Funding works differently in every country, but in the UK there's what UKSport gives out (a mix of some government funding but mostly cash from the National Lottery), and what you can raise yourself. And UKSport cash only goes to Olympic sports. Some sports like cycling and sailing have shed loads of both funding and sponsorship. Our shooters more or less get taken to the competitions, but have to pretty much fund their training and kit themselves. There's no money to employ them to train as pro-athletes. From what I know, most of them scratch around for individual sponsorship and augment it with part time work for at least the first two years of each Olympic cycle before they focus on the next games. There's lots of goodwill from their partners paying the rent and whatnot! They don't have the luxury of an Olympic Training Centre like the Americans have in Aspen.