His minigun had armor piercing rounds. There aren’t enough of them in the game to make regular use of this weapon with these rounds (at least from my impressions), but there’s plenty for this encounter.
By using AP rounds, which negate a great deal of this target’s high DT, and outputting a lot of lead, anything goes down eventually. But here’s what the crucial difference was between your character and his. He seems to have had the required strength for his minigun (a stat clearly visible) and the required skill level for the weapon (also a clearly visible stat). Without both, the weapon loses much of its damage and accuracy.
As for the Shotguns, with slug ammo they no longer spread damage all over the place, allowing you to concentrate it on a single weak point (head). Paired with a a perk that negates 10 DT (Shotgun Surgeon) makes them incredible weapons. They only suffer at range, having much lower accuracy than rifles, but in that last area range isn’t much of a concern.
And it’s not just the mid game shotgun. All shotguns were useful from the start. When meeting the (low) strength and skill requirements, you needed to get close and unload into the enemy’s head. Everything went down with one-two shots. Even using buckshot ammo (Shotgun Surgeon affects each individual slug). After you get/craft slugs it’s one shot kills to the head.
Varmint Rifle was awesome at the start, but only for sniping (with scope and without, actually). It wasn’t that useful in close up engagements.
But at range, sneak critical hits on a target completely unaware of your existence meant one shot kills on such foes as power gangers or viper gangers, rad scorpions, etc. The key was always to aim for the unarmored head and to fire undetected. Eventually you dropped the Varmint Rifle and picked up better stuff. And no, I never put a single point into sneak.
There’s also the reality that a Minigun’s projectiles are pretty much instant hit, which, despite the spread, makes it still useful outside of VATS. Not so much with the plasma weapons, which are very slow and hard to hit with outside of VATS. Yours was a plasma weapon. In my first play-through, with energy weapons, I dropped them fast and picked up a modded Laser Rifle, followed by a Trilaser Rifle. With most of my shots being made outside of VATS.
But as Virgil pointed out, the difference in weapons likely wasn’t actually your biggest problem:
Yep, this is key. Not only does it do less than optimal damage at below required skill, but below required strength it’s also very inaccurate.
