Categorisation vs. Classification
Let’s think about this for a second.
There are FPS-RPGs and RPG-RTSs (or SRPGs). Yet, I still hear people say that FPSs are the furthest things from RPGs. Despite Fallout 3, Bioshock, Deus Ex, the two genres seem irreconcilable.
Perhaps, then, ‘genre’ is the wrong term. Perhaps video games can’t be categorised, and doing so is butt-hurting more and more fanboys by the day.
So let’s move to the term ‘classification’. FPS, RPG, RTS, etcetera are classifications of games. Not genres or categories. They just describe the ways we can classify the mechanics of gameplay. ‘Genre’, then, would describe the style of the game (fantasy, steampunk, space, speculative, etc.).
This is a popular idea in other fields. In linguistics, the idea that a word must sit in a single category was done away with during the post-Chomsky days of non-binary semantic theories. Classification, as such, is what’s usually applied to words, like animals. This is because words are fluid things, like art and video games. The way they behave isn’t cut-and-dry.