The creature chosen at random isn’t targeted, so a creature with shroud or an opponent’s creature with hexproof can be chosen this way.
2024-03-08
Players can’t take actions between the time the creature is randomly chosen and the time at which the rest of the effects occur.
Choose a creature at random. You gain control of that creature until end of turn. Untap it. It gains haste until end of turn. Then destroy all other creatures.