WB is giving Night Dive permission to do it, Night Dive is the actual developers of it.

Basically ND asked for the source code to do the remaster, WB said "pay this stupidly large amount", ND said "No"
Atari said "then you have legal permission to reverse engineer your own version of the engine"

They legally cannot use any of the work that was done with BloodGDX as that is based off of a leaked blood beta and thus legally....dubious.

(as Paradocks pointed out, WB now owns the blood ip rights, not Atari, I am stuck in the past. Herpa Derpa)

As far as I know, it's Warner Bros that owns the code, so Atari has no say in this particular matter- they only have publishing rights.

Oh thats right, WB owns blood now, sorry I am still stuck in the past, I am going to edit my post.

https://www.gog.com/forum/blood_series/who_owns_the_rights_to_the_blood_franchise/page1

In short - the rights are a mess. Basically from what I'm reading in recent days - Atari has publishing rights to Blood 1 and 2 and "limited provisions for updating the game". WB owns the code and rights for any new game.
link.