Hunt the Mutant

 is a child's game played in Vault 101. A player is selected as the Mutant and hides while other players hunt for them. When the player is found, the game restarts with another player as the Mutant.

At one of Wally Mack's birthday parties in the 2260's, this game is played in the Atrium. Wally later mentions this game at the Lone Wanderer's tenth birthday party on July 13, 2268. By mentioning this game, Wally is unfavorably comparing his party to the Lone Wanderer's party.

Inconsistency

Due to Vault 101's original purpose in the vault experiment (being closed for 200+ years with no outside contact, that is), it is highly unlikely that any of the residents know about the Super Mutant threat or any mutations commonly known to wastelanders (like Ghouls or Radscorpions). The scouting reports found on the Overseer's computer reveal no hint whatsoever to super mutant activity at all. Given the experiment's purpose and the resulting oppressive nature of how Vault 101 has been ruled by generations of overseers, it seems highly unlikely that any resident would have been told anything about the outside world.

It also seems highly unlikely that James - knowing about the Super mutant threat due to his connections to the Brotherhood of Steel - has told the inhabitants (especially children) about the outside world since he could not even tell the the truth to his own son, the Vault Dweller himself.