I've only finished Vice City, GTA 4, and now 5. I have played some of the others, specifically 3 and San Andreas but never finished them. I got to parts in the games where I just got stuck. They do a lot better now creating missions that aren't semi-impossible to complete.
It's more about style and gameplay mechanics than the country of origin. You could have a company in San Francisco develop a Final Fantasy clone and it would be considered a JRPG. It's just a way of differentiating two styles of games that can be drastically different. And Europe is still considered to be part of the Western world so I don't think you need to worry about ERPGs popping up any time soon.