the thing is that imo "mood" doesn't apply to most multiplayer games, and especially games like quake, in the same way. of course competitive multiplayer games can be intense, thrilling etc, probably moreso than singleplayer games. but i dont think ive ever played quake 3 and thought "holy shit im in a postapocalyptic world shooting people with guns," even though i dont play with textures disabled.
Well, like I said, it's a matter of taste.
1) Quake 3 -- Well, I'd say that's more because Quake 3 has a very boring style, and the mood is mostly just "go-go-go!shoot-shoot-shoot!"
2) Mood in multiplayer games. Obviously mood has a place in multiplayer games. I think by mood you are thinking of moodiness. Every game has a mood to it. The mood might not be what is conveyed by the graphics, but its a mood that exists. Some multiplayer games are fast and frenetic (Unreal Tournament), some are tense and punctuated by short bursts of action (Splinter Cell).
And I think the art design should reinforce the mood of the game. I think that is a failing of Quake that the preferred way for high-end players to play is to mess with the graphic settings. If readability is the most important trait in Quake, then it should be emphasized by the art.