The Requiem IS a Mass.
In the classical music sense, yes. Really, though, and having performed it more than once with multiple interpretations, it's really more theatrical than reverent and was part of a movement that was corrected in the 19th century when chant was once again emphasized over "performance" level pieces, which the Mozart Requiem clearly is. This is part of the reason that classical music doesn't have so many Masses in the eras since.