IANAL but it's probably covered by fair use. Otherwise "Let's Play Videos" on YouTube would not be possible(and they actually show all the content in the game, while this shows single screenshots). Same goes for games review sites, Metacritic, game wikis etc that all have screenshots. It's definitely not in the interest of a game publisher to disallow the internet to show off their game, but they probably can't legally stop it either way.

Let's Play videos only exist because publishers allow them to. They aren't fair use. They could drop the DMCA hammer tomorrow but they don't because it makes them money.

Edit: obviously I'm not supporting this but this is the legal reality.

There are differing opinions on this from what I've heard. If the let's play video competes with the experience of playing the game then it seems like it would be as you say, but for many cases that would probably not be true. This is still not decided in court though and just because someone can DMCA someone else does not mean they are in the right legally. It would also be different in different countries, the free use doctrine and DMCA are a American concepts.

Virtual youtubers had numerous copyright infringement disputes with Japanese game studios for playing video games on stream. Hololive[1], the biggest vtubers agency, had to settle agreements (and pay money) with Nintendo, Konami, and capcom.

[1] https://en.wikipedia.org/wiki/Hololive_Production

IANAL, but I would expect that this could squeak by as Fair Use, considering the website is intended as a commentary on the various UI designs. If it's ever an issue, the fair use rationale could probably be improved by adding some descriptive text to each screenshot. In either case, the damages to the game publishers is minimal: what prospective game purchasers would see this UI database and choose to not buy the game?

Should be covered by fair use as it is for education and couldn't be considered a substitute for the original.

This is a good question and the first question I had in my head when I saw the site, especially as there is no info at the bottom of the screen other than "(c) Edd Coates 2020"