At least Dictionary.com validates the concept that "gyp" is from "Gypsy" [1]:
> Origin of gyp > An Americanism dating back to 1885–90; back formation from Gypsy.
Same with Miriram-Webster: [2]
> History and Etymology for gyp > > Noun > > probably short for gypsy
In either case, it is rude for the word to be used, contrary to what PG implies.