I hardly think I'm nitpicking about the Playstation 2 having some commercial life when it's still even seeing commercial game development and official releases from major publishers. And the Playstation 2 is only one generation old and is on the cusp of entering its 2nd post replacement console generation still kicking ever so slightly.
And I argued that entering its second post replacement generation doesn't automatically equate to classic. I didn't necessarily state that there are any present exceptions to that. I don't think there's any hard and fast rule here and like I already said, this thread and the many opinions and qualifications of the classic gaming community that have partly been expressed here is proof that it's not so simple. After all, this is only an ambiguous standard which the community decides on and typically argues about.
But I'd certainly argue for the Atari 2600 which lasted through two full console generations after its own (5200/Vectrex/Colecovision and then NES/SMS/7800/XEGS) and didn't see its commercial demise until into the third as possibly qualifying. And several certainly have gotten close if not made it commercially into its 3rd post replacement generation.
But the better examples are the ones that made it early for many. The Dreamcast for those reasons you dismissed was widely viewed as classic gaming years before its contemporaries, the Super Nintendo and Sega Genesis that were the last mainstream consoles that were predominantly 2D, the Neo Geo which I think was classified as such in the minds of the vast majority years before SNK ceased commercial support, etc.
For me personally, many qualifications I think are at play in my mind. Some of the major ones are has the system commercially died and how much time has passed since it ceased to have any commercial viability, is it commonly played by the average person or is it just kept alive by a few thousand classic gamers, what's the situation with both new and these days used stock at major retail chains, and what evolution has occurred with the switch of console generations.
There isn't just 1 factor at play and something like the demise of 2D gaming, for me at least, is going to make me quicker to consider a console and its respective generation as classic gaming material than something far less dramatic and different like this shift we're undergoing presently.