The Mac Mini is capable of delivering a very fun gaming experience, even on relatively modern games like WoW.
Sorry to rant here, but I assume by you saying WoW is "modern," I take it you mean a hardware intensive game? This isn't pointed towards you, but instead towards all of the silly WoW threads that pop up weekly...
This is the system requirements for WoW:
http://us.blizzard.com/support/article.xml?articleId=21054 . I don't understand why every Mac release we have to get a thread asking "will WoW run on my Mac?" OF COURSE IT'LL RUN ON YOUR MAC! The game is old! Blizzard has done a lot with the patches to improve the eye candy so that newer systems can take advantage of it, but damn... This game was running on Macs from about 6 years ago at bare minimum! *ahem*
But yes. Nintendo has already proven graphics don't matter. It's all about gameplay. (Although, with a game like Bioshock, an immersive story gets the job done, too.) But, Apple isn't a game company and not really a company that supported games all that well. Sure they wanted to bring Half Life 2 over to the Mac (according to the blog by IMG's editor-in-chief) and got EA to Cider-ize their games, but we all know Mac game performance ain't there. OpenGL and GPU drivers could be better, but Apple doesn't put in their full efforts on that anyway. Maybe if I saw some real effort in Mac gaming, I could try to support an Apple game console.
I want Apple in my living room, but I can't justify buying an AppleTV. Ever since the 360 added H.264 support, I've been using an external hard drive to watch my DVD rips of TV shows and movies. I only wish my iTunes content would be playable on the 360. I could see Apple partnering up with any of the three game console companies to provide iTunes content, but from seeing how Apple keeps iTunes all to itself, that probably isn't all that probable.
I'd also say there is room in the market for more competition, but it would take lots of risks, exclusives, and effort. If Microsoft or Sony can do it, so can another company. It's just the chance of failure is high by looking at some of the companies that attempted or dropped out of the console wars in the last two decades.
If there's any indication that Apple might be interested even in the slightest, it's those occasional game-related rumors we get.