Handicaps can be positive, e.g. in fixed distance racing one way to handicap is to "give" a starting distance to the racers who are slower than the scratch racer; in this system a higher handicap is more of an advantage.

Since the AI was playing scratch (the normal, unmodified play style), it seems odd to say it had a handicap. Rather, the human had a positive handicap of two stones.

Yes, but the title has an ambiguous parse (a shift-reduce conflict):

X defeats (Y with Z)

or

(X defeats Y) with Z

with the latter usually understood as meaning X has Z, as far as I know.