I bought my 360 about a year ago when GTAIV came out, pretty much for that, Forza, Fifa and Tiger Woods PGA Tour. I like sports games occasionally and having friends over to the halls to drink and play FIFA or Dynasty Warriors or Forza is fun. Do I play online that often? Not really, I play FIFA against friends and BF1943 when I feel like some 2003 flashbacks. The console was inexpensive (I got it with GTA3 for £200 IIRC), it's small and has a flat top (important when you need space and can use it as a monitor stand), can be output to VGA monitors (although I still haven't found a KVN switch that can hop between DVI and VGA connections without having to resort to keyboard commands) and is reliable (I got one of the later ones that has the improved hardware).
The PS3 was too big and expensive (although one of my friends is the biggest PS3 fanboy I've ever met, and hypes up positively mediocre and shallow games that I've seen time and time again on the PC) and the Wii didnt have GTAIV.
Most importantly my main gaming machine is my PC, and I didn't need a console that was all singing and dancing and had all kinds of super duper graphics technology in it, because I knew that my PC games could blow that fluff away on medium settings. I wanted an inexpensive console I could play sports games with my university friends on, and I think that's a fairly big demographic right there.