If chain\Gatling guns caused such massive recoil, they wouldn't be able to mount them on HUMVEE's, considering they aren't more than a few tons.
I don't think actual rotary cannons like the phalanx are mounted on the HMMVW, but rather on much heavier tracked vehicles. However, I don't think the author means literally "tons" of recoil, but rather "too much recoil for a person", which I imagine is true. Certain helicopters like the Super Cobra and some gunships carry rotary cannons like that, as do some medium armored vehicles.
The Japanese have already devloped a working power-suit Powered Armor isn't only a possibility, it's a reality in UFOAI. What is it in the game, 2086? 78 years to perfect this stuff is pretty simple. Definitely should have massive Chain guns roaring up, blasting away.
Powered armor will be a reality, for sure, but I doubt the point will be to field such large weapons. Rotary cannons need a great deal of ammunition to be effective; no human could carry the load. Anyone who's been in the army knows that your pack, your webbing, weapon, and ammo already weigh a great deal, and lightening this load is likely the objective of powered armor, not to arm soldiers with weapons only vehicles can mount (and carry enough ammo for). Ultimately, it's just a game, but I just think it would detract from the game's excellent realism. There's advancement, and then there's science-fiction. I really like that UFO:AI doesn't have super-weapons that make the game somewhat irrelevant to the realities of squad tactics. Even if a soldier could carry the weapon and the ammo, he (/she) would not be very mobile with it, and special forces troops are typically meant to be highly mobile.
That being said, there's no reason why mini-tanks or even APCs couldn't carry such weapons. How great would it be to see a futurized Bradley IFV leading the charge against aliens? I doubt we'll see that, but mini-tanks could be made quite awesome with long-range grenade launchers, missile launchers, and rotary cannons.