Not entirely sure I'd agree 100% with the definition. Whilst those games can fall under the classification of RPG it's a broad one; they tend to be referred to as hack'n'slash or the like. Compared to say the PC Baldur's Gate games the idea that CRPGs are less story-heavy than JRPGs is blown apart. The difference is rather in emphasis. The western stories tend to be a bit darker (Sometimes well, sometimes in the manner of an emo teenager, but darker nonetheless) and moreover they tend to be a lot less linear in both choices and outcomes. Whereas in FFVII your biggest storyline consequence was who you went on a date with, in a CRPG the entire game can be changed by choices you make.

An excellent example of this is in Fallout. If you make a character whose intelligence is 1 or 2 (out of 10), they are retarded. This completely changes how other characters treat you, completely changes the dialogue options and such open to you, and basically makes it a very different game in plot/story terms. Or the numerous paths through Morrowind which one could take, with other ways to complete the game even if you murder characters integral to the main quest.