This premise is utterly and completely wrong, CD. That's what the other posters are trying to explain to you.
The definition of a Game that you posted in your original post would probably NOT APPLY to D&D in court. D&D WOULD NOT be defined as a "GAME" in a legal way. Its contents are part game, part literature and part programming, in terms of legal likenesses.
The most likely is that the OGL, by virtue of being a legal document referring specifically to what is Open Content and what is Intellectual Property for WotC, is the document that would be used as a base to judge whether your document is a threat to WotC's IP or not.
You should really forget about what you, and you ONLY, consider to be mechanics you can or cannot reproduce. This line of thought is WRONG. Everyone is telling you so. I strongly suggest, for your own good, to not try to challenge this line of thought and just accept it.