All NM (including the trademark "Romex") is acceptable in an RV. The only wiring you will need to change if the PO ran NM is the extension cord.
Of course, all rules for NM wiring still need to be followed, and this type of wire can only be used where it is protected by walls, ceilings, chases, etc. and not exposed. If you need to run something exposed where it could be subjected to mechanical damage, you need to use conduit (metal or plastic) or metal-clad cable such as AC.