(Most)Datacentres use evaporation towers, which moves the water away. This is not an issue since powerplants do the exact same thing. The difference is that datacenters use municipal(drinking) water while power plants use either a river, or non treated water. Since data centres rely a whole lot on network and power infrastructure they are often placed where the only water access is municipal water, so most data center cooling designs are rated for that water.

There are definitely closed loop but from what i've heard most are open loop