Should I intervene when a colleague in a different department makes students run laps as part of their grade?
As an outsider this seems ridiculous. I think a quick email to the chair of the department saying that you have an advisee who is worried about BIO302 (or whatever the number is) and the running component. It seems reasonable to ask if that is actually a requirement (which it clearly is, but the department chair may not know it) and if it is, what course would be better suited for a student who is not interested in running. That should get the ball moving.
If the class is about microbiology, the students’ grade should depend on their knowledge of microbiology, and only on that.
(Edit: to clarify, “knowledge” covers things like lab skills and other things that have a connection to microbiology but aren’t strictly theoretical in nature. But not running. Definitely not running.)
I’ll assume based on OP’s description that this is taking place in the US. Even though I’m not a lawyer I would bet money that for the professor to tie grades in an academic class to athletic performance would constitute an obvious and blatant violation of one or more US laws. It very likely would also violate various policies of your university. For example, at my university the faculty code of conduct has a concept of “failure to meet the responsibilities of instruction”, which I know for a fact would cover the case of a professor spending a large amount of the class’s time on activities that are unrelated to the topic of the course.
Should I intervene when a colleague in a different department makes students run laps as part of their grade?
Obviously yes. You are the student’s undergraduate adviser. That makes you precisely the person positioned to help him when he is being treated in an abusive and probably illegal way by one of his professors.
How do I proceed? Do I talk to the dean? Do I talk to the head of the microbiology department?
Either of those persons sound like appropriate people to talk to. The chair would be the most appropriate, being the person directly above the misbehaving professor in the institutional hierarchy, so I suggest going to them, unless you have some specific reason to fear retaliation or other adverse consequences if you proceed in this way.
The professor of the class is a long time professor at the university. He is known for being a bit zany.
This is irrelevant. If the professor graded his students based on their looks, how much money they have, the number of hot dogs they can wolf down in 10 minutes, or any other similar criterion unrelated to their knowledge of microbiology, we would not be talking about the professor’s zaniness. Neither should we be talking about it in the current equally absurd scenario.
How much leeway should a professor be given to determine what "counts" in his or her class?
Any leeway a microbiology professor should or should not be given would be appropriate to discuss in the context of how they teach microbiology, and how they evaluate students’ knowledge of microbiology. What the professor is doing here is entirely unrelated to such activities, and as such, no leeway applies. As with the mention of zaniness, “leeway” is not even a relevant factor to discuss.
The student's health status or physique is not of consideration here. If the situation is as the student described, the prof's behavior is simply untenable -- if for no other reason than 25% of contact hours being spent on nonsense. Every student in the class should be incensed. The TAs should be upset that they're spending their time this way.
The chair of the relevant department is the appropriate point of contact. When communicating with the Chair, include that you're passing the student's story along without verification, but you felt the story odd enough that you felt compelled to bring it to the Chair's attention.