I think there should be a general option for flagging on the "off-topic" section. How to flag a question that is not game-related if not?
This conversation from The Bridge seems to be relevant. It seems that those of us with less than 3000 rep are unable to (directly and clearly) flag for general off-topic-ness not covered under our three custom off-topic reasons, discussed in this meta post.
One option we do have further back in the question flagging tree is "other (needs ♦ moderator attention)". However unless the question is egregiously off-topic, and no other flag reasons apply, I tend to leave it up to our 3k+ users. Their close/reopen vote privileges are considerably more effective than simply flagging, they have an option for a custom off-topic close reason, and as many a disgruntled user can attest, the 3k+ users we have here on Arqade are by no means shy about putting questions on hold when they find it necessary to.
At certain times during the day (usually late night for the north-american time zones), user activity drops off, and off-topic questions tend to stick around longer than they would during peak hours, but they are all handled appropriately in time.
One last option available to us is to stop by The Bridge - this is where most of our regular (and by extention, usually high-rep) users hang out. If no one else has already, you could call attention to the question either by linking directly or replying to the feed bot (Lazers)'s message containing the off-topic question; politely suggesting that the question is off-topic and close votes would be handy.