2040s XCom is related but barely. After the first alien war was won, XCom was kept going for a short amount of time (to make sure it was over) and then turned into an Elerium scavenging organization. After crashed UFOs on land had all been taken care of, underwater operations started. When that started to run out too, XCom was privatized and bought by a rich dude. That XCom looked little like EU XCom we know for sure.
At the beginning of the 2nd alien war, they had only one base and diving equipment. But XCom's owner convinced the funding council to reactivate XCom as an international strike force, which is when the player takes control.
Since their base are above water and they can be expected to engage aliens above water, it would make sense for them to be given whatever is the regular infantry arsenal of the 2040. While that certainly isn't plasma and alloy-based armors, it is much more likely to be some sort of firearm (or even mass produced lasers) than harpoon guns.
Your argument makes a lot sense for the quality of troops in TftD and the lack of tech from the original (except maybe lasers, depending on if they were mass produced or locked away after the first war), but it doesn't cover needing to engage aliens on the ground with weapons that are designed for underwater engagements. That still makes no sense.
@yrizoud: Indeed, that and being an oceanographer (loved Cousteau when I was a kid!) makes TftD my favorite.