The reason for this is that the guns in Doom were 2D Sprites, so making the shotgun pump, or super shotgun reload was done with relatively normal 2D animation techniques.
Animating a 3D model is an entirely different process, that requires a very different skill set, so early 3D games kind of cheated when it came to some things. Quake there reloading or pumping the shotgun on screen. You look at GoldenEye 64 instead of having a reloading animation you just lower the weapon off screen and the Reload is implied to have happened.
It took a few years until games like Half-Life 1 had proper reloading animations for 3D weapons.