I'm not english native but "Do you know the game rules" shouldn't be accepted as well?
Yes and no. The meaning is almost the same but the Duolingo version includes the possessive (genitive) form "rules of the game."
It sounds a bit odd...more like a literal German-English translation (for example). "Rules of the game" sounds more natural!
Does the "to the" and the "of the" alter the case? "of the" being accusitive...
I understand that - I was wondering if the suggestion of "to the" being acceptable would alter the Duo sentence. понимаешь?
Technically "the rules to the game" would be translated as "правила к игре", so the case would be Dative. But there's not much difference, and "правила к игре" is not a common expression, so most would translate it as "правила игры" anyway.