Looks nice, with neat workmanship.
120V wire connections not in an electrical enclosure are not up to NEC spec. That does make work like this tricky, since there are practically no boxes and often little room for them in an RV. You might be able to get a shallow box and regular receptacle and put it in place of the TV outlet—or maybe use a (partly) surface mounted one if there's enough clearance behind the TV.
Do be aware of how much power the fireplace consumes when it's heating. If you have other high-current devices on the circuit, you could find you pop the circuit breaker. I guess if that's a problem it will become obvious enough with use...just might be something to think about. I suspect most factory RV fireplace installs have a dedicated circuit, or at the least very little else on the same circuit.