The organisation just sent over a statement that says its Tanooki-related Flash game was all a tongue-in-cheek joke, and that it really wishes the real-life inspiration for Super Mario 3D Land's most famous suit could fly and tail-whip like its in-game counterpart.
That's that cleared up, then.
PETA Statement re New PETA Game Lampoons Skin-Stealing Mario
Mario fans: Relax! PETA's game was meant to be tongue-in-cheek, a fun way to call attention to a serious issue, that raccoon dogs are skinned alive for their fur. We wish real-life tanukis could fly or swat enemies away with their tails and escape from those who profit from their skins. You can help them by never buying real fur.