What does BM stand for in Gaming?

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.