What does that mean to you?
Not much, other than the person saying "design has moved on" is wrong. They're trying to couch heir personal preferences/tastes in terms of some kind of theory about the history of RPG design that doesn't hold up to scrutiny. RPG design itself isn't analogous to technology, so there's nowhere you can really go with that argument.
I read statements of that kind as: "I like X and not Y". I accept them as true, I'm happy to read the reasons why a person likes X (and not Y), because it's interesting to see how different people react to and use different gaming techniques/mechanics/abstraction & resolution methodologies, but --so far-- I'm not convinced those reasons can ever add up to a demonstration game design is progressing to an objectively better state.
On the whole, production values have gotten better thanks to technology, but the rules themselves? Nope.
Is game design a science or an art?
Art with a side of math.
What elements are "improvements" to you?
Transparency with regard to goals. For example, I really digging 13th Age right now, because it's very clear in what it tries to do. It has openly game-y bits combined with openly narrative bits and does a pretty good job at explaining why they're there.
Are any of these things merely fashions?
To an extent, yes. And that's not a bad thing.
Absolutely. The classic example is a lack of social encounter rules. It's a serious flaw to some gamers. It's a feature to others.
Is the reason older games get played less simply because they are less supported, or because they are not as good?
I don't think support is a big issue. With the ease of finding fan-created materials/active fan communities for almost any given system online, I can't think of a truly unsupported system these days.
I think the simple answer is: people's tastes change. And then change back. I've been running AD&D for the past 2.5 years now, after a 15-year hiatus. As DM, I'm
loving it. But 2 of my players miss the the more player-option rich systems we were playing beforehand.
So at some point, I imagine we'll switch back.