What uses of the name of a video game don't infringe on their trademarks?

Anything that falls under fair use.

Ex. "Pac-Man Fever":

https://youtu.be/XY_ESTnBlS0

When you started your post title with "when", I thought you were telling us something.

To make it a question, you'd need to move the "does" to right after the when.

When does the use of the name of a video game not infringe on trademarks?

This depends on the laws of your jurisdiction. Generally, there are exceptions for fair use, meaning you could use the name for educational purposes or satire, etc.

Did you have any specific examples in mind?

I think the legal bar would be whether or not consumers could infer that you are associated with the company who makes the game being named.

https://en.wikipedia.org/wiki/Fair_use_(U.S._trademark_law)

It needs to have a different name than other games. It means you can't pick the same name somebody else already picked for their game or product.