First, before I say anything, I'm 28, single, not even an uncle of an older child, so no experience. On the other hand, I've played games since age 8 and I was a bit of a journalist in that area for several years, so I know a lot about games.
Firstly, please note that games per se aren't sinful. They aren't any more sinful than comparable ways of playing or having fun by children. The medium doesn't make them sinful (not any more than books or films or comics etc.), the content may (and interactivity can matter to a certain extent, as opposed to more passive watching or reading, where you don't enact anything but merely imagine it).
I'd say much depends on the age of the child. Age categories stated on boxes (along with warnings about specific categories of potentially objectionable content) are a hint. I suppose a child shouldn't be kept in a shell when it comes to challenges that don't exceed those that are out in the street or in books or films that you'd allow him to read. Thus, I wouldn't hold back a 15 year old from playing a game with a sticker saying "age 15+, strong language, reference to alcohol and tobacco, mild violence" (that's basically as problematic as any film out there, or less), unless the child exhibited problems.
What I see as a child exhibiting problems is getting addicted, learning bad habits from the game, visibly enjoying the objectionable parts of the game while taking them too seriously, becoming more aggressive, dropping in school performance etc. A 12 year old boy in army fatigues barking contemptuously at adults certainly is having problems! A 15 year old boy replaying replaying World War 2 battles or reclaiming hostages from a building occupied by terrorists and loving it is not.
I wouldn't really worry about boys playing war games any more than dressing up as cowboys, Indians, policemen, knights etc. and "fighting" (like small cats that "kill" each other 20 times an hour). Back in the time boys from certain families were actually riding into battles managing the equipment for a knight from age 14 and that knight might have been 21 himself. And they surely did practice beforehand. There are still boys who aren't even legally adult before they sign up for the armed forces. There's also SCA and renfaires (reenactment groups). Nothing wrong with that. If it's about knighthood, manhood, leadership, strategy and tactics, defending one's country and so on, I'd see a war game as good rather than bad or neutral. (In fact, being fun is also a good reason to play a game, within reasonable limits. :)) It's a version of cops and thieves, cowboys and Indians (boys pretending to shoot other boys just because they belong to the wrong race), the knight and dragon and princess fantasy.
The same could be said about roleplaying games, except they can be troubling to certain consciences depending on the specific game and especially one's way of playing it, especially given the modern trends in that particular branch of the gaming industry. Personally, I'd be unable to recommend a "clean" modern title, even though I know a lot about roleplaying games since they were my favourite type, although I know there are Catholics who are able to play some titles without being bothered. An important thing here to understand is the "role" aspect, which is comparable to acting in a theatrical play, where things do not happen for real, and for the child to be mature enough to handle well whatever comes his way in books, or films or games.
I'd suggest gathering information about a particular troubling game (Googling a review or two, watching screenshots or videos from it, asking friends who have seen or played it) and taking it relatively easy, without being too agitated (at worst you'll have to veto it). Banning war games broadly would be a bit like banning war films or war books (some of which are probably in the school curriculum for the relevant age). It could also be a dramatic event for a child who really liked games (imagine being forbidden to read any comics because some can be bad. This is not to say that keeping an eye isn't needed (again, like with books or films) or that games are typically innocent (there's a lot of bad stuff, some of which a child may be unable to handle properly).
If any of the terms or expressions or references I use is unclear, please let me know and I'll explain it. Similarly, if you'd like to ask any questions, I'd be glad to answer. This forum also has a "Popular Media" section (in "Catholic Living", just like these family forums) where you can ask about a particular title. I sometimes do that because I have no desire to play anything that mispresents the Church, refers to the occult or revels in needless violence.