You don't have a true quadsport. Sports have kick starters. You remember when Kawasaki came out with the Lakota, it was a Mojave with racks and auto trans. Yours has auto trans right? Thats what your bike is. I don't know the actual nomenclature, but it couldn't be too hard to find.
1985 ATC250ES
1985 ATC250SX
1984 ATC200S "Little Red" - Trailer hitch, Hondaline: Front and Rear Racks, Cooler Rack, Tripmeter, HL Grille, Rubber Footpeg Covers, Mudflaps.
1985 ATC70
2008 CRF230L - Dual Sport
2016 TRX500 Foreman Rubicon Deluxe