Could've been better
The idea of this is pretty good. The levels look pretty nice, I especially like the layering you did in the background and using the original sprites makes it breathe oldschool, which in this case is a good thing.
The collision detection is a bit iffy at times. Sometimes I shoot through enemies because they're too close and dying & restarting is a pain because you're stripped of all your weapons. I realize this is how it was done in the original but that's where you could have done a concession to keep gameplay up.
Besides these minor gripes there's something else I'd like to address. A few things that worked well for Doom (no vertical aiming for instance, and enemy behavior) don't transfer that seamlessly into a different genre. The fact that enemies can be on a slightly different vertical plane than the barrel of your gun, something you can't well compensate for if the enemy's lower and you're already standing on the ground, creates a form of artificial difficulty that doesn't help the gameplay.
The way spectres act worked fine in Doom because you still had 3 other directions to move in (back, and to the left & right) but in the platformer it's a different matter because you're standing on the ground and the enemy's in your face. If you happen to be in a low corridor or backed against a wall that leaves you only 1 other direction to move in.
These kind of things don't transfer directly between these 2 game types and they're things that can make or break the game experience. If you attempt this again, that's something to take into account and take steps to remove those problems.
On the whole, it's a nice enough attempt though.