They're just like any other data center, except bigger because that's more efficient than building a bunch of smaller ones.
AI data centers have a lot of GPUs and specialty hardware that use a lot of power, but they're still just big buildings with lots of computers in them. They just sort of sit there, with air conditioners running 24/7.
If they're not the huge "hyper scale" type, you end up with a situation like in the article: Where they had to cram too many cooling units in too tight a tight space (to make up for the fact that the data center wasn't built for its current workload).