Have you considered a raspberry pi?
There isn't much love for them on these forums, but I'm using one right now, and it should do everything you listed above just fine.
It's not an ideal all- round Mame solution, and I intend to go with a conventional PC at some point, but as I said, it will run those games fine, and has the advantage of being cheap and tiny (ideal for a bartop) and requires no cooling fan.