Something I think a lot of people fail to consider when categorizing games is the actual systemic design of the game in question.
Rather than trying to group games by commonality - all RPGs for example follow a similar structure, thus to be an RPG you must possess the same systemic components as other RPGs - they should be grouped by apex system aspects.
The way I do it is thus and in this order, labelled by common genre designation, system aspect and then a game with is something of a paradigm example of the genre:
1) Strategy - The system, the body of the games infrastructure and raw informational depth [Civilizations)
2) Roleplaying - The system mask with makes the otherwise blank data system appear to the player as a fictional environment [Final Fantasy]
3) Platforming - The environment itself, which is the level design, the placement of world objects and the flow of the virtual occupants [Mario Galaxy]
4) Racing - The control system, the interface, how the user manipulates that which is within the gameworld and the degree of finite control required of the player [Gran Turismo]
5) Combat - The interaction between the world elements; when one object encounters another, what results? Be the exchange between sword and shield or car bumper and wall. [Tekken or possibility Devil May Cry]
All of these components are part of any game to a greater or lesser extent and could be used to classify a game by how much detail is given to any specific aspect, i.e. a roleplaying game, above all else, is focused around the game's setting and story. This because of course no game is entirely based around, for example, strategy as even the apex example above includes elements of roleplaying (a system mask) that makes the gameworld appear to be alt-earth history rather than bland gray teams of variously attributed units directed by the program user.
In this way you are not limited by the inherited design of game system - which is to say that just because you're making an RPG, you don't NEED to include a modified D20 system (static character classes, levelling, grinding, etc) for the combat mechanics - but instead can create innovative gameplay which nevertheless serves the purpose of any given aspect - you could create a combat system with the purpose of gameworld entity statistical comparison that can either be a modified D20 system or something entirely unique.
Plus with this kind of genre definition, from a design perspective, you gain the advantage of modular conceptualization, which is to say that you can consider the gameworld setting apart from the combative system and try out multiple variations of each - consider that some MMORPG's employ both third person traditional RPG style combat as well as typically RTS style topdown combat. This division of individual system components is similar to how c++ object orientation programming functions; plug n play modules.
I'll definitely give this lot a read as there must be a more organized way of game categorization rather than the likes of every other gamer inventing his own designations, and I certainly don't believe that such products of math and logic should not classified by types, although as I say, grouping by design is more intelligent and dynamic than grouping by similarity, in my opinion anyway.
If anyone has any counterpoints they would like to make...?