There's definitely gaming in the pallouse. Most of em are part of (or game with) da Mommas Boyz gaming club.
http://damommasboyzforums.yuku.com/directory
They have a club house in Moscow, so it is close but not super convenient to Pullman. There forum is a good place to start lookin though.
About all I can tell you about the Pullman area but if you come up to Spokane there's 3 stores to game at:
Merlyn's -- the oldest game/sci-fi store in the area. Excellent selection of games, comics and a very large play area. I think Wed is their
40k night and they have a tournament maybe 1-2 times a year. Located in downtown area and close to I-90 so would be very convenient for you.
The Battleground -- Gaming store with a narrower focus then Merlyn's (no comics, movies, etc). They run quite a few tournaments during the year, usually coinciding with a new army release. Thursday is their
40k night and it is usually very very busy. They can be found off of Market Street not far from I-90
Hobbytown -- Chain store but a good portion of the staff are gamers and they have the biggest selection of product. No
CCG gaming so they are the place to play
40k on a Friday night. Rarely have tournaments (maybe 1 a year or less, that may change though). Farthest drive for you but if you are in Spokane on Friday they would be the place to go.
Also check out
http://www.nwgamers.org/. Not a lot of traffic but you might get additional info there. Tournaments at Battleground and Hobbytown are usually announced there.
HTH