I come speaking from the experience of being one of the other 'villages' that a poster mentioned higher up, vis a vis being a public librarian in a high-youth, low-income area. A few things I'd like to say after reading this thread.
1) The OP does not actually give (and looks like was not given) a complete description of what this program entails. Making assumptions from the list of requests is merely that, making assumptions. Perhaps the board games are going to be used as rewards. Or perhaps used to help gain trust or teach lessons on fair play or strategy. We don't know, so claiming that these requests are evidence that the kids will be sitting around playing fun games is really making a leap. Likewise for making assumptions based for a half hour of one day during a lunch time experience made by a teenager.
2) Saying since it doesn't help your kids directly it is not a direct help to you so why should you get yourself involved with it is such a myopic, strange view of the world. Children who stay in school longer and more successfully mean adults who are less likely to commit crimes, live under the poverty line, or be incarcerated, all of which do, in fact, benefit each of us directly. The world is not all straight lines or tidy little cubicles, it's a web. You may not see the other side of the web, but when a string gets pulled, you will probably end up with the vibrations.
3) The single most telling factor of a child's success is not anything the school does, or the community does, or anything else. It is the parents involvement. Problem is, no matter how much you as a parent are involved, that does not mean that all parents are involved. And there is no way to force parents who are uninterested or unable to be involved. All you can do in those situations is try to find some way, minimally effectual though it may be, to replace that all important involvement with some sort of substitute where the child will get expectations, involvement, support, and safety. Without these things, the chances of even a driven child or teen to be able to be successful becomes very very low.
4) In our community, there is nothing for teenagers to do. The community center even closes its doors to teens that are there without parents. Which means that they flood our library. Most of them are great and we adore these kids. Some of them are problematic because they frankly do not want to be there, but its the only place to go (for a number of reasons including 'locked out because parents are at work', 'parents can't be home so they'll watch you at the library, free babysitting (hah!)" and 'my dad is drunk and if I get in his hair he'll beat me' as well as plain old teenagers not wanting to be in the house all day, shocking, I know). Sometimes, even the great kids act up (don't say you didn't when you were a teenager, I will stare at you squintily) and we have to kick them out. Frankly, we cannot provide all that they need, because what they need is attention, goals, activity and support. If parents can't/won't provide them, someone has to. It sounds like that is what this program is attempting to do.
5) Yes, there are a lot of bad/ineffectual programs out there. But just because some don't work or waste money doesn't ipso facto mean all of them won't work and will waste money. What needs to happen is that there be an understanding of the goals and a metric to measure them. Better oversight, better auditing, and better metrics are what is needed, not just to throw up one's hands and say that it's all doomed to failure from the start. But seriously, if a hundred kids enter a program and even five of them have their lives changed for the better... how is that worthless?
6) To pull yourself up by your bootstraps, you actually have to have boots. Every parent out there who has the ability to care for their kid should thank their lucky stars that they do, and not bitterly deny a child a chance that they otherwise would never get because it is somehow 'unfair' that that child gets anything because they are neglected, abused, troubled, or disabled. Your child has a good support system, loving parents who work hard and sacrifice for them, and a bright future even without any help from the schools or other outside agencies. Don't spit on a kid who doesn't have those things and did not choose not to have those things.