Firefox has been able to block all third-party / cross-site cookies for ages. It’s just not the default because it breaks some sites. But dive into the settings and you can easily set it to block all cross-site cookies, or even all cookies if you prefer.
Absolutely love this game. Played it from beginning to end on the PC multiple times over the decades. The original floppy version that is, not the poncy CD version he’s using! 😂