Thanks for the update. It doesn't look exactly the same, since for me it's more like bouncing described by @advowson above. But still it's good that you are working on cross domain referencing of fonts. It's a known issue that can affect Firefox.

Yes, HTTPS Everywhere should not cause this problem, since it automatically gives up on security if the server keeps issuing bad redirections. Forced HTTPS through NoScript can definitely show the symptoms described. It affects me regularly. Before the problem started, I always browsed the game pages of any new offering and for most sales. Now, I often don't, since hitting a bad server causes the game pages to loop and fail to load.

I mentioned this to support once before and received a generic "We're looking into it." Since the problem still happens, I don't think it was investigated very thoroughly. All the servers, both good and bad, answer under the hostname www.gog.com, so I can't tell how many are good and how many are bad, but the failure rate is high enough to be so frustrating that I gave up on reading game pages.
It's not a problem with the version of Firefox. It's a problem with the servers issuing bad redirects, but you only notice it if (a) you inspect whether you stayed on https or (b) you use an extension that keeps you on https. If you use plain Firefox without security extensions, you'll be quietly switched to insecure http and the site will seem to keep working. This is fine if you only browse GOG from secure Internet connections. If you browse from a public Wifi hotspot (e.g. coffee shop), best practice is for you to stay on HTTPS connections, which is much easier if you configure the browser to do it for you.

Strange thing is that I don't have NoScript and any other similar add-ons besides HTTPSeverywhere and Adblock Plus. And even when both are disabled (through their UI, not completely disabled) this still happens. And yes, lately it became very common and it's very annoying.

Dumping cookies & reloading has worked the few times I've tried it.

A bit late to the party, but I had to say this - it's getting pretty tiresome that whenever a Firefox user experiences a problem with the site, the first thing that you suggest is: Firefox is not a niche browser and it'd be appreciated if you took it into account from the get go instead of trying to figure it out afterwards.