D&D and its derivates
A PnP created from a video game
A highly specialized LotR game. Although I am a bit surprised about this one.
I can't help but notice you have to keep adding qualifiers to your definition. Now we can't use something based on a video game (because video games aren't modern?), or something that's "specialized", whatever that means.
Also bear in mind that to defeat your claim that there are none, I only need to provide one example, and I have done more than that. The above is not intended to be a complete list. That would take much more time and effort than is worth here.
One point that you have continued to ignore is that D&D and its derivatives remain very popular, likely the most popular. That implies that, even if your definition is accurate, it is inconsequential. So what if a game is "modern" by your shaky definition? If modern gamers still play "non-modern" games, then your definition of modern games needs work.
And you also didn't address the point that classless games have been around since 1975. If something invented in 1975 is modern, surely something invented in 1973 is as well, since you want to bring timelines into it.
drothgery makes a good point, though
He does make a good point, and damages your claim that classless games are necessarily "modern". They can simply be an attempt to differentiate themselved from other games, without being any more advanced or what have you.