Complex sentence: The base's movie theatre was disassembled and reassembled on the campus of what is today the University of Missouri-Kansas City where it was the Kansas City Playhouse until being torn down for a new theatre.
Split into simpler sentences: The base's movie theatre was disassembled and reassembled on the campus of what is today the University of Missouri-Kansas City. It served as the Kansas City Playhouse until being torn down for a new theatre.