Watching some of the better play-throughs shows it pretty well: https://youtu.be/P6J352J_RG8?t=10202
Those were some of my favorite parts of Quake 3 too. The maps where you could spring off a jump lift from one end of the map to the other, shooting at people as you soared through the air...
Also, I actually liked the (much more limited / less frustrating) platforming mechanics during fights, that just gives you more freedom of movement. Freedom of movement is good and Doom'ish.
It's the part outside of them, where you have to hop around in silence just to get somewhere, or get to a juicy item, that's objectionable - because that part is less about freedom, and more about railroading ("No, you HAVE to jump onto that moving train to proceed... and sorry, the last checkpoint is before that fight that you just have - hope you like replaying it if you fail the jump.").
I absolutely hate the platformer aspect. Seriously, guys, just because you have taught Doomguy to jump, doesn't mean that I want to have a series of random platforms that have to be jumped on in precise sequence to get anywhere.
At first I thought it's just a gimmick that they were showcasing in one map, and it'd even out... instead, I found that I'm spending more and more time doing this, and it's getting harder and harder, with the addition of moving platforms etc. The first Hell map was the last straw.
If I wanted to play Super Mario, I'd buy that, not something called "Doom".