Depends. It's not as bad as Dora the Explorer theme song, or Barney.

Part of living with someone is learning to tune out a lot of otherwise annoying things.

That said, if the gamer in question insisted on blasting 1st person shooter or war games all night at full volume while other family members needed to sleep, then yeah, that would be annoying. But again, the annoyance is the callous disregard of the rest of the family, the obsession, and the disrespect, not the actual game.