I keep seeing a phrase like "BM fatigue" in hearthstone stream chats in twich. The context is that the streamer's opponent dies from fatigue and the whole chat says that phrase... So what does BM stand for?
In Hearthstone, along with most online competitive games, it usually stands for "Bad Manners".
Basically, it means someone is spamming taunts, being a bad sport, or drawing out a game when they can either win or concede just to prolong the game unnecessarily because they're salty[upset] about a loss or want to toy with their opponent a little longer before they win.
Without seeing the game you're referring to, I can only assume the opponent had no chance of winning and let himself die to fatigue just to deny the streamer the "final blow" rather than just leaving the game.