Dead? No. But certainly far from dominant like it once was.
When I started seriously playing games, if you wanted to play online it HAD to be a PC game. It wasn't until the Xbox came out that console games started to match up with PC games in terms of general game quality and multiplayer potential.
If there is a problem, it's the simple fact that in order for a PC to demonstrate it's superior graphical capability in a game these days it has to have a lot of power behind it, which results in expensive and all too frequent upgrades. Couple that with the fact that very few games are PC exclusives these days and you have a recipe for disaster.
I still use my PC for some games. I generally prefer shooters in PC for example but I no longer cry when I try to play them on a console. Strategy games can really only be rightly played on the PC as far as I'm concerned. While I believe that one could create a successful MMO for consoles it has yet to be done, so when I'm in the mood for a second job I turn to the PC for MMO offerings.
As I've gotten older I've become less concerned with playing games in their "ideal" state though. These days, when I'm not working or what have you it's nice to be able to throw a disc into my Xbox and play a game online for an hour without having to fight with hardware settings or drivers or any of a dozen other little annoying things. To make matters worse, my gaming PC is getting a bit long in the tooth and there has yet to be a new PC game that makes me think I need to bother replacing my system to play. Sure there's Crysis or Far Cry 2, but nothing I've seen about either game seems terribly interesting.