Deathtouch (Any amount of damage this deals to a creature is enough to destroy it.)
Whenever a creature you control with deathtouch deals combat damage to a player, that player gets two poison counters. (A player with ten or more poison counters loses the game.)
Losing the game because a player (preferably an opponent) has ten or more poison counters is a rule of the game. Fynn doesn't have to still be on the battlefield when someone (preferably an opponent) gets their tenth poison counter.