Does the war2tv page say you are streaming only when streaming war2 and not other games?
Not currently, if they're playing some other game OR playing war2 but at desktop/in channel then the stream shows this icon:
and this one if they're in game lobby or playing:
It's possible to do, I chose not to because 1) a lot of new streamers don't select any game, and 2) it's not uncommon to switch games then forget to switch back, and I'd rather have a stray game show now and then than potentially exclude any legit stream. Most war2 streamers don't stream anything else so it's not a big issue, I'll only occasionally see archangel or EQ (and now Geno on sc2) playing something else