I get why most modern sites are designed the way they are. I wouldn’t want my bank nor government websites to be cartoony.

However game websites are going to be used heavily by people familiar with the game. Also, if the game UI is unfathomable then people aren’t going to like the game anyway. So you would expect any website that borrows from the game UI to also be discoverable.

Personally I think a large part of the change was due to the shift to responsive websites. Back when everyone was using a 5:4 monitor you could get more creative and use things like absolute positioning. These days everything needs to be distilled down to the lowest common denominator because you cannot make any expectations about resolution nor aspect ratios.

Add to that how the mouse cursor have been replaced with fat fingers, and you now require the site to be tolerant with input devices that cannot navigate fiddling controls.

You could see the contrast back when sites first started doing a mobile versions of their site (before Google threatened to give poorer ranking to such sites).