I think some of the exceptions can be instructive.
For example, Sumo.
It could be considered a territory game or a goal game or it could be considered a fighting game. As the primary purpose is to move your opponent to a certain boundary and not attrition I think I might steer away from the fighting game aspect.
Also Paintball.
This seems like a combat game as it simulates combat, but it also has elements of territory and goals. It also has elements of shooting/accuracy. Which element takes first precedence?
What about Chess?
Strategy is it’s most talked about aspect, but it also is a representation of combat in which elimination is key.
Motor sports is a bit of an odd duck.
It’s easy to simply lump it in with speed games but there are a handful of motor sports that don’t involve racing much at all. What about tractor pulls? There’s a speed element but the primary aspect is strength which makes it more similar to weightlifting than racing. Rock climbing and motorcycle acrobatics are grace games more than racing games.
In the case of motor sports which difference is more instructive? Should we classify by “motor sport” first therefore grouping all the above examples together or should we classify by goal first which would fragment motor vehicles into “speed”, “strength” and “grace”?
Snow sports could be grouped similarly. Is the fact that it occurs on the snow more instructive than the fact that it’s a race or that it’s a acrobatic event? One might argue that the ski jumping has more in common with downhill skiing than it does with the long jump.
What about water sports? Do you want to group wakeboarding and jet ski racing together? Is jet ski racing more like motorcycle racing than it is water ski jumping?
Is billiards more similar to curling than it is to say chess?
How the heck do you categorize lumberjack races? Tree cutting races are about speed and accuracy but I can’t say that are very much like the hurdles, I might say they are more similar to shooting.
One might make all “tool games” a top level category, grouping shooting games, lumberjack games, paintball and darts into one group.
Do you put snowmobile racing closer to skiing or closer to motorcycle racing?
Very tricky, perhaps focusing on the object or the objective aren’t the right way to think.