It says "Ongoing: This minion is not affected by other player's abilities."
Now, I understand that the Game Guru is not affected by other player's minions/actions abilities.
What I'm not sure is if another player wins a base that can destroy the Game Guru is that a legal target? I am not sure if a captured base counts as a player's ability.
Other player abilities is only from their personal cards, not effects from bases, so the Game Guru can be affected by them.