It's not a parody, unless you take parody to mean 'copy of an artist's style'. Parodies are not a tribute but an insult to the person concerned, usually an exaggeration - this is just a copy.
Parody doesn't have to insult the original; the key thing you need is commenting on the original. This piece is on the border between using the setting and style of F&T to make an unrelated point (not parody) and commenting on how the F&T cookies story, despite being written for children, makes a broader point about incentives and control that adults would do well to internalize (parody).