because it’s Sting’s singing on P Ditty’s recording.
That’s what sold the record, not that it was written by these song writers that the public doesn’t hear of.
Actually, look at the last paragraph. His voice isn't on it, only Andy Summer's guitar is on it. (Sting may have performed it with him at some point.)
Sting also admitted Summer should have been credited as a cowriter, since he added a lot of the music.