As soon as the installer is elevated, it can install services, drivers, etc that run with high privileges forever. Like, for example, Galaxy. If you run a malicious program and say yes at the UAC prompt, it's game over, permanently.

And as I said, if you run a malicious program and don't see a UAC prompt, that doesn't mean it hasn't bypassed UAC using various bugs or by-design back doors and installed permanent malware on your computer anyway. UAC was created by Microsoft to pressure software vendors to structure their software in a particular way. It doesn't actually provide any significant security to the end user.

Oh, get real. You plan to discover malware by manually looking at every network connection your computer makes? Besides the fact that it would take you a day to review the connections made by the adtech in one random webpage these days, and that if GOG Galaxy was malicious it presumably would use the same exact connections to GOG servers for C&C that it does now, even if you find something you basically have to throw your computer in a dumpster.

This is a stupid argument. If you want to make it your full time job to inspect GOG's installers for malware, you may or may not find any that's there. None of this bears on what I said at all: running untrusted installers is dangerous and puts a lot of trust in the signer of the installer, so GOG shouldn't piss away that trust to get their galaxy install numbers up.

No.
sudo disagrees. And UAC is quite similar to sudo.

I'm not. I say that a properly set up firewall can (and does) protect machines from unauthorized connections. But properly set up firewall is not the same as "built-in" firewall.

And again, yes, running untrusted installers is dangerous. There are ways to mitigate said danger, if you have reason to believe that said installer is untrusted.
Bundling Galaxy to a game installer is not making the installer untrusted, unless you specificall don't trust Galaxy. In which case, you do have the option of dissecting Galaxy communications and seeing what it actually does. Unless of course you don't care to find out whether it actually is dangerous, but drop it just because it may be (which means dropping almost everything, including bluetooth, WPA2, PGP and RSA keys).