As long as that player was attacked this turn by an Assassin you controlled, Ramses, Assassin Lord’s last ability triggers when that player loses the game for any reason, not just due to combat damage. This is true even if the Assassin is no longer on the battlefield, no longer under your control, or no longer an Assassin at the time that player loses the game.

If you attack an opponent with a non-Assassin creature and that creature becomes an Assassin after attackers were declared, that player was not “attacked” this turn by an Assassin you controlled.

Similarly, if an Assassin enters the battlefield under your control attacking a player, that creature didn’t “attack” and won’t cause this ability to trigger.

For the last ability to trigger, an Assassin you controlled must have attacked the player. Attacking a planeswalker the player controls won’t count.