Does anyone know if there happen to be any games which are only for the Linux platform?
Try a google search for Linux Games. There are lots of 'em out there, but not knowing your preference for type of games, is too broad to answer.
I like Sauerbraten, which is an FPS.
Battle for Wesnoth also comes to mind quickly.
Nexuiz has always been my favorite, and there are a few commercial games.
Vendetta is very similar to EVE Online, I think the rate is about the same as well and it has a native Linux client.
The same goes for Enemy Territory Quake Wars, it has a native Linux client, I think it retails for $40.