The joke fails on its own internal logic.
If they had agreed to a "dog fight," and Israel admitted that it was a crocodile, then Israel would be disqualified.
If they had agreed to any "representative animal," then Hezbollah would, like Israel, have focused on more ferocious animals.
Excuse me, you transphobe. That “dog” can be whatever he/she/it wants to be. If it identifies as a dog, then dog it is.