I don't think I agree with this. I much prefer your earlier definition - "character's abilities are among the things shaped by the player." IMO this is enough to distinguish strategy/wargame from (C)RPG, where the player does not in fact shape the character's abilities - if he does in some way (see HOMM) then you've introduced RPG elements into your strategy/wargame, and then where the game falls on the axis depends on how much importance you give to these RPG elements; if they're a very small focus it's primarly a strategy/wargame (see Panzer General), if it's the main focus then it's a pure CRPG (see Pool of Radiance), if it's somewhere in-between then it's a hybrid (see HOMM). Of course it's not always entirely clear (see Warlords 3, which I consider to fall somewhere between HOMM and PG), but nobody said that a definition has to have every single game fall in its own box; as long as vast majority of games fall somewhere on the axis then you're fine. The nice thing about my (well, your, but since your stated definition shifted slightly from it I'll appropriate it as mine) is that it can as easily apply regardless of the presence of combat, so it can also be used to distinguish between adventure games and CRPG's too (since in adventure char's abilities are beyond player's control, and in fact are utterly set in stone), and with a bit of tweaking can also easily integrate action-RPG's: where direct player input supercedes character's abilities in shaping the world, but char's abilities still play a major role; as their role lessens you instead shift towards "action game with CRPG elements", but you're still on the same axis.
Extra bonus: my definition can also easily be integrated into Mondblut's (or vice-versa) as presented in this thread. It also completely bypasses the storyfag/mondblutian dichotomy (as well as the linear/openworld one for that matter), since it does not in any way rely on combat-heaviness or story-heaviness; the only caveat would be whether combat is influenced more by player or character skill (see action-RPG above), and likewise for story/dialog (therefore PST is not an adventure game - I can already see Mondblut disagreeing with this one though). You can then have fun splitting the genre into as many subgenres as you like based on combat vs exploration vs story vs C&C vs action vs dungeon crawling vs whatever the hell you want, but while it may be trickier to get everything lumped properly into neat subgenres I think using the 2 axes that I have already mentioned, plus maybe a third for story vs open-world, would allow for a pretty well defined categorization even for subgenres, and you'd be left with very few games that don't fit anywhere (and these probably won't fit regardless of the system you try to design).
