Blood Tyrant's second ability causes each player to lose 1 life, including you. Blood Tyrant will count each player's life loss, including yours, when determining how many +1/+1 counters it gets.

Blood Tyrant's third ability will trigger no matter how a player loses the game: due to a state-based action (as a result of having a life total of 0 or less, trying to draw a card from an empty library, or having ten poison counters), a spell or ability that says that player loses the game, a concession, or a game loss awarded by a judge.

In a multiplayer game using the limited range of influence option (such as a Grand Melee game), if a spell or ability says that you win the game, it instead causes all of your opponents within your range of influence to lose the game. This is another way by which Blood Tyrant's third ability can trigger.