That is a nice easy and manageable way to define a genre but it is ultimately misguided. It is an oversimplification used to try and fit something complex into small easy to understand terms. It is very tempting to do that and it is very easy just to accept this method because in general all the other genres are this easy to understand. Racing games, shooters, fighting games, manager games, sports games and puzzle games. These are all easy to define. Role-playing-games however is an entirely different beast. I think the reason is that the term was not created as a label for a computer game genre but as the name of a hobby completely distinct from computer games. What this means is that a CRPG should be defined as a computer game that most precisely emulate a true RPG (otherwise known as tabletop RPG or LARP for those into that sort of thing). As for stat-progression and the like: Well....bismarck55 said:
Character progression (as being distinct from character development) is part of most games out there. There are some notable exceptions (point and click adventure games for example) but in most games you character grows more powerful as you go along. They gain new powers, weapons or similar things. In your average RPG they usually use the system you mention to separate player knowledge from character knowledge. This is just an extension of the normal growing power of the protagonist and not the quintessential part of the experience. The quintessential part the RPG is the ability to shape who the character is through choices and decisions (and the resulting consequences). If a game does not have these parts it ultimately is not an RPG.