There is no punchline. You haven’t been setup for a joke. This happened in real life and what you are about to see is what the guy had to go through to get the eel out of his butt.
The cameras weren’t rolling when it got in there somehow, so we don’t have the luxury of knowing that end of it. It appears that he got drunk and POOF! An eel ended up in his butt. You can speculate all you want about how, but it’s so rare that any of your guesses would be a strong possibility.
He could have eaten it when it was young and it grew inside of him. He could have gone swimming in eel infested waters and a baby got in his shorts, and then found its way swimming up a dark canal it had never seen before. There are literally millions of possibilities.
The fact of the matter is that the eel was in his butt and it was time for it to come out. So, he went to the doctor because they’re proficient with this kind of stuff. In medical school, they take a class called “Getting Things Out Of People’s Butts.” The class is pretty short. All anyone really needs to know is how to use a salad tong without also dropping it inside the anal cavity, which would then require an additional salad tong to get the original one out first.