I was kind of startled that the example of this super-jump was used as an example. So 4e reduced this "Primacy of Magic" by...giving rogues magical powers? WTF?
Either way you slice it, yes.
If you look at limited-use martial maneuvers that have power rivaling that of same-level, same-recharge magical spells as meaning the martial power must be magical, regardless of what any fluff text says, then, well, there's /nothing but magic/. How can something meaningfully rank First in a list of one?
If you don't go there, if you accept that martial powers aren't magical, even though they're extraordinary, and rival the power of magic, then, well, magic isn't top of the list, either, is it?
Either way, it wont "feel magical" anymore, because it's not "just better."
There needs to be a gap between the two, to bestow Primacy on the correct one. It can cut both ways: it can notionally 'balance' by making powerful/critically-important magic limited in meaningful, but manageable ways, so that it can be used when it'll have the most impact, but, not just all the time. Vancian does that. Anti-magic is another layer of it. Spell interruption used to be a component of it, that concentration echoes however feebly, etc.
Every other edition of D&D gives you magic that's very powerful, limited (less so with each successive ed, but still) in manageable ways, juxtaposed with non-magical options that are less varied, less potent, but limited only by the need to be alive and conscious to keep using them. That supports the Primacy of Magic.
(And that's not even getting into magic /items/ which 1e & 5e, in particular, do a really good job of making feel particularly magical - and 4e demoted to glorified fashion accessories.)
And I also don't like people highjacking threads for their personal wars, even if they start their latest edition wars by saying, AKTUALLY, IM NOT HERE FOR AN EDITION WAR, BUT IM GONNA THROW SOME LOGS ON THE FIRE!
I try to avoid edition wars. Just because I burned out on 4E doesn't mean that it was a bad game, it just wasn't for me at least not when it got above the initial tier of play.
But I know a lot of people that felt that the edition just didn't "feel" like D&D. It had a lot of things in common with D&D. The basic structure was there, so why did it feel different?
One main reason is that the rules were too "tight". In some ways that was a good thing but it didn't leave a lot of wiggle room. As a DM if there was a power that could achieve something, it always felt a little bit like cheating if someone could just replicate a power through improv.
So I would say another aspect would be ease of customization and creative play. A player picks up a gnome goblin and starts swinging it by it's legs like a club? No problem! Make up a rule that makes sense or use the improvised weapon attack.
That flexibility also applies to styles of play. As much as there are some never-ending threads about how to play if you take 10 different groups, each group is going to have more in common than not. But they are each going to be played slightly differently. TOTM? All grid all the time? Lots of in-person RP or just describing what your PC does in third person. It's all D&D.
Different classes just "feel" different. A paladin plays different than a rogue, a wizard has different concerns than a fighter. That wasn't true in 4E, with everyone having the same basic structure.
Related to that, you can have characters that feel special but not supernatural. A champion fighter is just a guy that wades into combat and swings a weapon. It may not be very realistic, but it's one of the classes that you could throw into a movie set in the real world and it wouldn't look too out of place.
I also think alignment as a simple hook is iconic. Yes, I know it's overly simplified but it does give me a quick starting point, particularly for monsters. I know a devil will be slightly different from a demon just based on alignment.
So while 4E had the sheen and look of D&D, it was a different game and just didn't scratch the same itch for a lot of people.