Will Exquisite Blood trigger even if the life loss eliminates the player
Player #3 will gain 100 life.

The fact that #8 is no longer in the game has no effect on Exquisite Blood's triggered ability. All of its effect was put on the stack when #8 lost 100 life. It does not require #8 to be in play when it resolves, because it does not check for any current information about that player. Even if it did, rule 800.4g would take effect:

If an effect requires information about a specific player, the effect uses the current information about that player if he or she is still in the game; otherwise, the effect uses the last known information about that player before he or she left the game.

Only effects that require a target are affected if that target is no longer legal or does not exist anymore; they would be countered in that case.