Ah, now I'm picking up what you're putting down.
Personally, I'd move the sixth generation of consoles down into vintage games simply because of the massive shift that the industry underwent with the jump to the seventh generation of consoles. That generation saw the introduction of elements like HD gaming, digital distribution, DLC, microtransactions, an increased focus on online gaming, AAA development becoming a massive financial undertakings that only a few studios can afford to develop, indie games becoming widespread (especially on consoles), the rise of mobile gaming, the death of consoles having well-defined libraries (as swaths of old games from previous consoles are continually ported to modern consoles), free-to-play games, live service games, and the United States once again overtaking Japan as the center of the gaming industry for the first time in 20+ years. I guess the Wii could also be included with the Gamecube, PS2, and Xbox in the vintage category because it lacks so many of the features mentioned before. Althought, it feels weird that one seventh gen console would be vintage and the other two would just be old but not retro, so I'm just going to ignore it for now.
I think the term "retro" is fine for describing the era from the NES to the seventh generation, even if that's technically not using the term properly. Games from the "retro" era definitely have a different feel to them for a variety of reasons. Dev teams were small and games had a limited amount of space, so games feel a lot more creatively focused and that they're more than the sum of its limited parts. Alternatively, we just have hindsight and can forget the shit on the market. I'd be tempted to call this era the "Golden Age of Gaming" like with comics, but this name might be too self-righteous.