Chef Shudder'thun is definitely a meme deck. While it can be very powerful, it is mostly for fun.
There are multiple win conditions. The obvious one being depleting your deck and using Mecha'thun to wrap it up. You can kill Mecha'thun by either saving up a Hagatha's Scheme after it has been reduced, or if he has been pulled by Jepetto Joybuzz he can just get hit by Zap! to finish it up. The 2nd option is obviously ideal.
Another great way to win is Chef Nomi. Get the deck depleted and throw him out there.