So one of the features is real time 3D and that made me raise an eye brow. To my knowledge the only 3d version of this game is the Sega Saturn version. The PSX and PC got build engine version. Or am I wrong?

The PSX and Saturn both use real time 3D engines, the PC version uses Build.

Looking at the Wiki it does state that the PC version is based on the Build Engine, while the Saturn version uses the original development teams Powerslave engine.

Could anyone confirm which version this release is?

There's nothing about the original platform in the notes.
edit: they've confirmed on twitter it's the build engine version

It says its powered by DosBox, so it must be the original DOS PC release.

The Saturn version specifically used the SlaveDriver engine, and the Playstation version had it's own engine, written again from scratch.

It's the PC version.

Did they fix the controls?

I dunno but you might as well use one of the modern ports - PCExhumed or PowerslaveGDX

They did not but using PCExhumed they work just like a modern game.

How do you get the music working in BuildGDX?

I would assume the BuildGDX Readme says how to do that.

3D means three dimensions, length, width, and height. Actually this game could be called 4D since there is time. So-called 2.5D games (I really dislike that term) do actually have all three, so calling this 3D isn't necessarily wrong. I know the 3D is faked, but these are computer games we're talking about, and modern 3D engines are more advanced, but still fake, not actually 3D either.

Build engine supports Room-over-Room. I don't know if it is used in Powerslave.

Blood has RoR and its maps are not strictly 2.5D like Doom.