Because he's a classy guy, and that's the traditional way to issue a proper challenge to fisticuffs: That's where the expression 'the gloves come off' originates. For bonus points, slap your enemies across the face with them before you start punching.
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Logo uses joystick by liftarn
And you don't want icky gunpowder residue on your skin, hence the gloves.
Daemon blood on the other hand (or possibly both hands, chest and face)... Great for the skin, allegedly.
The brass knuckles don't fit over the glove.
I don't think he's wearing a glove when holding his pistol.
As shown in a comment below, he is.

Three decades of graphics development and no one has come close to this level of arm hair realism.
Ok this is more obvious. In the image OP posted it's quite hard to see.
I've never played doom so I have no frame of reference. But I feel the op image was intentionally cropped deceptively because I had no idea what I was looking at either
Ngl, I thought it was a dick
edit
Typo
Nah, you see very little of Doomguy's arm in the actual game.
Two left hands, one with and one without glove.
Duke Nukem had at least 3 legs. He could kick with two legs while still being able to walk around and even jump!

I’ve got a third leg. And it’s looking to kick your ass
Sounds like something he’d say.
Bet they are kicking themselves for not recording that
He was using his penis.
Yeah, this was just obvious lore.
He might just have digestive issues and really good balance. Maybe a hovercraft skirt sewn onto the seat of his pants.
I loved doing that
And they laughed at me when I said Doomguy was related to Goro.
Cut vs uncut left hand
This makes me uncomfy
It's his armhair, just a slightly different perspective
He was probably just a heavy smoker, skin like leather. Checks out for the time period.
Thats not a glove; his wrist is jist extra wrinkly when holding guns.
But also: He puts on a ring with a spike on it, too.
No glove, no love
Yeah, it looks like a glove, but maybe it supposed to be skin folding when you hold gun on the belt/stomach level? The skin will fold similarly if you do.
He's definitely wearing gloves. You can also see it on the plasma gun recoil sprite:

The shotgun:

And especially with the super shotgun in Doom 2:

And for good measure, these uncropped pistol sprites are in the "vault" thingy that came with the latest Bethesda rerelease:

You're right. My bad.
Thanks for explanations and including the art from the game, nice to see it as I haven't played it literally in decades.
plasma gun
One of the first "aha" design moments I ever got was the Doom plasma gun. There was a kid's toy version of the American M-60 Light Machine gun that I had. The back half was pretty cool on its own, the typical thumper machanism to make noise, but it also had secondary triggers in the stock and a little gear that would advance a belt of soft plastic ammo. Didn't do anything except move, but the effect was cool.
The front actually came off, and was a pretty decent quality suction-dart shooter. However, if you turned it around and used the the mating surface as the "muzzle..." BOOM! (or "ZAP" I guess... lol) Doom plasma gun, down to the exact number of ridges.
"The gloves are off!"
Sometimes you just need to make that personal connection
:O I never noticed that.
... Nor that doom guy is left handed. :O
He's also wearing brass knuckles on the punch, or at least something spiky! Never noticed that before
Maybe its a flip mitten kinda deal