Actual heating due to human energy use is not really a big deal except perhaps locally. Climate change is caused by changing how much heat the earth retains from the sun. Maybe if we stopped using fossil fuels and used immense amounts of nuclear power, we would care about the waste heat. But solar and wind power largely redirect energy flows.

It’s kind of like how brine from desalination is not a global problem for the oceans at all — all that matters is diluting it enough that it doesn’t poison the local ecosystem.

This approach appears to directly reduce energy use (that's what the articles says). The heat would still be going into the local environment, but if there is a reduction in energy use, there should be less of it.

The temperature is independent of the actual heat flux. Also - a quick search suggests that at best the data center coolers run at COP of little more than 10. The inverse of that is the amount of heat wasted just on cooling. Having a system not relying on heat pumps would only make it better. A back of the envelope calculation based on PC AIOs suggests they would achieve a COP of 20 or more. A scaled up system would be more efficient than that, if not just for wider tubes.