Here's the thing: if we keep all of these games sorted into their originally defined generations, with each leap of technology duly noted, it will VERY quickly become unwieldly. It's also worth noting that, by modern standards, these leaps of technology don't look as impressive. Of course there's a notable difference between Atari 2600 & Intellivision when you really look at them. Go grab a 10-12 year old and see how much they care about those differences.
In order to prevent the history of gaming from turning into the ring cycle of pop culture history, we must condense things down based on what's notable to us now. The introduction of cartridges was definitely notable. The appearance of Nintendo, at least Stateside, was EXTREMELY notable. These are, in fact, sensible places to stick the new goalposts. Those who want to learn more in-depth can research and learn about generation 2.5 and 2.8, or early/mid/late 2nd gen, or however you want to call it.
And yes- I do think there's more redefining in our future. You can already see the lines of the 8 & 16 bit generations running together, I'm sure someday they'll merge into a combined generation, with the divide moving to PS1 and the birth of CD based gaming (with the Sega CD and the Turbografx CD marked as historical oddities- the pre-CD CD-based systems).
I get why it upsets people- if you grew up with this stuff, you don't want to see the things that mattered in your youth discarded as unimportant. But that's life, guys. Time happens to everything. Case in point: Go google 'middle ages' & see how much damn time we're running together with THAT one!