Likely, he’s been rewarded with attention when he howls while someone is using a computer. Reconditioning the antisocial behavior entails rewarding him for the social behavior you prefer.

Kill a few Minecraft dogs in front of him, then whisper “you’re next if you don’t pipe down” at him.

You’ve wrongly linked the behaviour with an action. Beagles yell regardless of what you do if you’re not paying them attention.

Try telling him this: Woof! Woof woof! Bark woof grrrrr woof! Bark bark rrrrrrrr bark raa raa raa woof.

woof.

My dog absolutely hates certain noises. Anything excessively high pitched especially.

Have you tried turning the sound off, or is it you being on the computer in general rather than playing Minecraft?

Do you play any other games? If not, it may be the higher load than normal causing the fans to spin, and maybe that’s messing with his ears.

The only other thing I can think of, besides the dog simply seeking attention, are your actions while you play Minecraft. Whether you make noises or yell, fidget, gasp, move in your chair a lot (squeeky wheels?) etc.

He’s a beagle, so he’s stubborn and not willing to negotiate

Well have you tried offering him a turn? You’ve been hogging the controller, let him try.

Does the dog get upset when you have headphones on? If it’s a beagle the sounds and or music may be messing with it’s ears.

You can’t. Play Terraria instead.

@LaunchesKayaks it’s probably a seating issue.

Get one of these chairs

Invent Minecraft for Dogs.

Feed him some rotten flesh

Yell back

Play Minetest and see how he reacts.

Get him a BeagleBone Black!