After checking a few sites, it looks like AMD may have between 20 and 37% of PC market share. I do not consider that "tiny."

This attack as it stands does not seem to apply to Intel server hardware from Skylake to present due to a different interconnect architecture, though the researchers indicate a belief the attack may be portable it would also be more limited.

Complete rectal estimation here, but I'd imagine executive laptops to probably be the next juiciest target as the end user station most likely to contain "interesting" data. While AMD has been making incredible inroads in the laptop market with Zen 2 and especially Zen 3, as opposed to the Bulldozer era when seeing an AMD sticker on a laptop let you know it was the cheapest one on the shelf, they still haven't made it to the models commonly bought by businesses.

AMD is absolutely killing it in the DIY desktop space, deservedly so (this post typed from a 3900X that I love), but on the OEM side of things you still generally have to go out of your way to find them in anything not marketed at gamers.

Fact is Intel takes the brunt of these attacks because their HW is more available especially in semi-standardised environments like universities. Also, Intel fund researchers (this paper was part funded by Intel), and their technical documentation is better than AMDs, at least in my experience. That makes it easier to understand the CPU internals, which is a big part of these papers.