Cool.
That's a big part of what tags are used for. There is different things a tag can say. Game mechanics, story, interface options, art style, certain topics of interest and so on. And some tags will say several things together.
Those diagrams are game mechanics. There might be some for story as well. Maybe there are some for stories in general and not just games. Like how cyberpunk is a sub genre of science fiction. I think the diagrams are not that deep there, like a western has not all that many sub genres. But crossovers like steam punk plus western. Of course for games, there are games that have no story at all or only some superflous fluff. Most of those will be in the arcade or puzzle genres I think. Also, classical card games like Poker.
If you have a poker game set in the wild west about a women trying to run a business, you would have tags about mechanics (poker/card game), the setting (wild west), the protagonist (female protagonist) and about how it is a business simulation. And if such would be super popular it might even spawn it's own tag that says "a game like that." And that tag might warp over time to mean something different. (Read history of the tag rogue like).
The game might have tags about how it is 2d, in pixel art and because it has perma-"death" and you would collect different bonus items on each "run", people might even call it rogue like. It has controller support and is fully voiced. And then you have the pixel art be anime style as well and the love interests of the female protagonist be women and you would use yuri as a tag.
Tagging is complex ;-) And why someone would like that hypothetical game is hard to pinpoint. It would be like saying someone likes a certain food because of which spices it contains.