Send-ups of television series have become a cottage industry in New York theater, but they usually target familiar, long-established properties. Dylan MarcAurele’s Heated Rivalry: The Unauthorized Musical Parody arrives barely six months after HBO Max premiered Heated Rivalry, a hit drama about rival hockey players who become lovers. Under Alan Kliffer’s direction, the result is fresh and bawdy, and sung with serious voices by a talented cast, all of whom help with scene changes that boost the production’s sketch-comedy vibe.