Titanium was designed to create native apps on multiple platforms, but that doesn’t mean, that one can’t create a game using Titanium. In fact, there are some modules that will ease game development using Titanium Appcelerator. The best represent I've found was QuickTiGame2d module which allows to implement game logic using scenes and sprites, and I tried it out by creating simple game named “Gorodki”.
You can read more on my experience with this framework and detailed explanation of development of this application in latest issue of JSmag. You can use coupon code to get this issue for free: 123483y (valid for about 20 uses).
And you can check out resulting code at http://code.google.com/p/gorodki-using-quicktigame2d/