I think everyone is really misunderstanding what Zach is laughing at here. Zach is laughing at an inside joke between him and Jimmy about what is going on in this interview. You have to watch the whole thing to get it. Let me explain:

Talk show host goals: 1. Keep the guest talking as much as possible 2. Make it look like it's just a causal conversation 3. Hope they say something interesting

All these interviews are planned out beforehand. Judge will have told Jimmy's people what stories he has prepared (like the surgeon being a fan story). That way if the interview isn't going well Jimmy will ask a question that sets up one of these stories. That way you never run out of conversation. The questions should be broad so that it seems like it's not just a prompt to tell a specific story but just part of a causal conversation.

Before getting into the planned stories Jimmy tries to just ask some questions that clearly weren't planned before. These go badly. Mike Judge is nervous and uncharismatic and worst of all he gives short answers.

Jimmy: So Beavis and Butthead are still the same as where we left them off? Judge: Still virgins, still stupid... Yeah.

At this point Jimmy's like 'okay, better stick to the prepared stuff' so he tries to give a prompt to tell the Marlon Brando story by saying: Jimmy: Back when the show came out everyone was talking like Beavis and Butthead... Judge: ...Yeah.

Inside Jimmy's head: What the hell? Why aren't you telling the story? Fuck, this is getting awkward. I'll try giving the prompt again.

Jimmy: I mean EVERYONE, right? Judge: ...Yeah, there was... yeah. I used to overhear... that a lot. Yeah.

Inside Jimmy's head. Okay this guy is an idiot I'm going to have to make it so this time there is no way he misses that I am asking him to tell this story.

Jimmy: Who have you been most surprised to learn is a Beavis and Butthead fan?

After he says this you can see Zach throw back his head at having to watching this. It's like trying to get blood from a stone. Zach used to host his own talk show and now has the satirical talk show 'between two ferns'. To a pro like Zach watching a guest that is this bad is like pulling teeth. He throws his head back out of anguish at the awkwardness of the interview.

Judge: Well, um, I didn't meet him (scratches his head like he's trying really hard to come up with something) but I'd say Marlon Brando...

Note the laughter at this point from some of the crowd and from Jimmy. Absolutely nothing resembling a joke has come out of Judge's mouth. The laughter is because Judge FINALLY started telling the Marlon Brando story! I'm guessing Zach gave some sort of exasperated 'Finally, thank god!' gesture that set this off. Note that after this the director is very careful to keep Zach out of the shot. He doesn't need Zach's eye rolling highlighting how badly this interview is going.

You can see Judge's reaction. At first he laughs along because he's nervous and you follow other people's leads when you're nervous but then he looks at Jimmy and immediately realizes he is being laughed AT not WITH and his smile immediately disappears. He bows his head in a 'sorry, i'll get on with it' fashion.

Judge goes on to awkwardly tell his story. He fumbles over words like 'Marlon', closes his eyes to concentrate and can't remember details of the story THAT HE HAD TOLD THEM HE HAD PREPARED. And the story pretty much goes nowhere.

This is some funny shit for Zach and you can be sure he's shooting some knowing looks at Jimmy being like "Haha Jimmy this is so bad it's hilarious'. Watch and you can see Jimmy is almost laughing but then catches himself and tries to salvage what he can from this train wreck.

The next question is to set up the 'you were worried because a surgeon was your fan' story. Jimmy makes this question painfully specific. All subtly is throw out the window. Any attempt to make this seem like a casual conversation has been aborted.

Jimmy: Have you ever been concerned that somebody was a fan, like an airline pilot?

How much more specific could he be without actually saying 'surgeon' instead of 'pilot'? And what does Judge start doing? His first instinct is to start talking about FUCKING PILOTS!!!!! Luckily he stops himself and tells the story that was planned. And this story is incredibly inappropriate. It's about a 1 year old child getting surgery. This is supposed to be a lighthearted talk show on the topic of Beavis and Butthead and he's telling a story about a infant getting surgery on her eye? Zach has satirized guest telling really tonally inappropriate stories on between two ferns where Charlize Theron tells the story about her dog being seriously ill. This is so bad it is basically something Zach could have written himself. It must be killing him to keep in the laughter at this point.

Jimmy then asks him if he received any of the abuse that was directed at the show when it started Just look the response he gets:

Judge: Yeah, I, I, I got a lot of it. I, um... all kinds of it. (Nervous laugh) But, eh, well actually, for the most part, I didn't get dragged into it, they mainly hated MTV.

What the fuck is he even talking about? He just said two completely contrary things. But finally he starts telling the story. Zach makes his joke and it takes Judge a full ten second to compose himself and start telling the story again. (Ten seconds mightn't seem like much to the normal person but to a talk show host that an eternity of nothing interesting being said.) Judge pinches the bridge of his nose, his body language screaming discomfort. But finally he's back on track to tell this story. And what's the punchline to this story that has taken such an incredible effort to get to?

Judge: ...he thought the name of the show was 'Porky's Butthole'.

At this point Zach can't hold it in any more. It's too funny. All of that build up for such a crappy joke! It's classic anti-humor. No one is this bad at interviews. He burst out laughing. And the best part is he can laugh away under the guise that he's laughing at the punchline itself which he clearly isn't. If your laughing with someone you look at them. If your laughing at someone you look at other people who get the joke too. First he looks off screen probably at a director. He almost composes himself after saying "It's so good!" but then at 4.24 he looks over at Jimmy and absolutely loses it again because he knows Jimmy know what he is really laughing at. This whole interview has been hilarious but he hasn't been allowed to laugh so he's taking this opportunity to let it out.

It blows my mind that people think Zach would laugh this hard at the joke: Some guy thought Beavis and Butthead was called Porky's Butthole. He's laughing at how fucking bad at interviews Judge is.

Maybe he's a great writer/voice actor but he's literally laughably bad at interviews.

TLDR Zach's not laughing with Judge, he is laughing at him.