From the article I thought the helium was used mostly for cooling (where I imagine the purity wouldn't be that important)

But what other processes do the fabs use the helium for then?

It is used a lot for cooling but in many systems its used without a classical heat exchangers where the helium is isolated from the workpiece.

Helium is pumped beneath the wafer to keep it cool so any impurities can leak through the chuck seal into the chamber above and disrupt the process. It’s also very precisely controlled so impurities change the uniformity of the thermal conductivity of the gas, creating hot spots on the wafer.

In EUV it’s used to both to cool the optics and as a buffer gas to manage debris from the plasma so any contaminants can deposit on the optics. At 13.5nm even a single layer of hydrocarbon molecules can create problems and the light bounces many times between mirrors so the error compounds.

There are many places where helium doesn’t have to be as pure but contamination events and surprise maintenance are so expensive that it’s not worth the extra savings (or the risk of mislabling and using dirty helium in the sensitive parts).