Also not a lawyer, but in the past, I did a lot of research into how intellectual property works in the United States.

I've heard it over and over that trademark owners are legally required to defend their trademarks from potential violators like this, or they can lose the trademark.

This isn't entirely true. As long as the trademark is actually renewed, it doesn't need to be aggressively defended.

There are a couple of reasons why they might choose to defend it regardless. One of the major ones is to deter other entities from thinking they too could get away with violating it. An actual, legally-relevant reason to defend it would be to prevent the mark from genericization. That's when a trademark like a brand name colloquially becomes used to refer to an entire class of products, such as with the Escalator™.

For an example of a company whose trademark was at risk of genericization, look no further than Nintendo. They saved it by defending the trademark tooth and nail while using marketing to reinforce that their product is the Nintendo and not a Nintendo. If people had kept referring to video game consoles as "Nintendos" like they used to back in the 80s and 90s, another company may have been able to successfully challenge the trademark and opened the flood gates for products like the "Microsoft® Xbox 720 nintendo". Nintendo the corporation is still a bunch of overly-litigous assholes, but back then, they actually needed to be.

In Eminem's case, it's probably as a deterrent. Unless people have started referring to Caucasian rappers as "eminems" without me noticing, his brand is at absolutely no risk of being genericized.

Everybody knows this

Everybody "knows" some bullshit that isn't actually based in reality. Pieces of shit spread it so players like Disney seem less unhinged, but is absolutely not required. Renewing your trademark is the only requirement.