The Good, the Bad and the Munchkin proves that no genre is immune to Munchkiness. While the Old West has been popular in literature and visual media it's definitely been a secondary interest among RPGs. And there's really little precedent for the "dungeon crawl" style of gaming in any kind of Old West setting.
Maybe our posse of Munchkins are exploring a "ghost town?" Of course, ghost towns really come after the Old West era and probably suit Munchkin Cthulhu better.
It doesn't really matter of course, as the whole genre thing is just an excuse for more jokes, bad puns and cultural references by opening up fresh material.
The game play is the familiar Munchkin pattern of open a door, fight the monster and collect the treasure/loot the room.
As in the other human-centric games, there are no races in tGtBatM, just four classes: Cowboys, Dudes, Indians and Outlaws. I think it's fairly safe to predict that every Munchkin series game will always have classes because they will never pass up the chance to say that every character "starts as a human with no class."
Compared to other Munchkin series games, there aren't as many ways to hinder your opponents when they get close to victory. There are only a few "monster" enhancers in the deck and a limited number of one-use-only items that can sway the course of the fight, so unless you happen to have a wandering monster card and a monster in your hand at game end it may be hard to stop an opponent. This gives the game a somewhat different feel from most of the other Munchkin series games where the first player to bid for victory often gets smacked down hard which clears the way for the No. 2 player to succeed on his/her bid. Perhaps when the inevitable expansion comes out it will provide more options for messing with the other players.