Hmm, that's odd. I would suggest trying to run the game manually, rather than from Steam.
You can find those files under /Users/Yourname/Library/Application Support/Steam/SteamApps/common/ai war fleet command/
Running AIWar.app takes Steam out of the equation, in case there is some sort of funky conflict going on there.
Hopefully that works, but in case not I really wonder if the game is launching on some display that is currently disabled or something. If you have an extra display that is sometimes on, but not in this specific instance, for example. I'm not an expert on the Mac, and I've never heard of anything like this (usually the game either runs or it doesn't), so I'm kind of shooting in the dark. Sounds like you have a mildly usual setup, but that's something that the engine we use -- Unity 3D -- should more than be able to handle.
If worst comes to worst, you can always install the game directly from our website, using our OSX installer, on top of the folder above. That way, if Steam did corrupt the files and it just can't tell, you can fix them that way. I really can't see that Steam would have been able to check anything useful in 4-5 seconds, it's just not possible. Normally a verification takes 10-20 minutes or more.
Hope that helps...