I think I’d be more concerned about this card leading to stall strategies. If a player has accumulated a decent amount of ghost rock, they can waste several minutes having him enter and leave places. Yes, the opponent gets money, but if they have nothing to spend it on and there are 5 minutes left in the game, that’s not an issue.
As for an infinite loop between two players each with their own copies of this card, my first thought (as a programmer) was that he’d probably be a key component to someday making Doomtown turing complete, like Magic!
Oh, and I find it kind of amusing that he can also visit saloons out of town as well! Well, at least one of them.