And why does it look like I now need to allow access to that domain for the website to work properly?

Now this is a good question. The website should work without the need to access any website aside from GOG's own.

I was asking myself the same question. A quick websearch turned out that this is an error tracking software for a few languages: PHP, Javascript, Python, Ruby. Maybe more?

Their customer list has a few big names like Adobe and Uber. So apparently not an "evil" site after all. Still, I'd rather not have to whitelist them for Gog to work.