So my notions are consistent with the usual ones. When you say that baseball involves more luck that basketball your notion depend on the entire scenario and reward systems and not just on the rules of the games.

No. Orthonormal said nothing of the sort. He just listed ways to check whether a game is skill or luck based, and didn't claim that the critical factor is the reward system.

I suggest you spend less effort trying to look like you were right all along and just admit, "Okay, I used the terms differently from how they're normally used." Is it really that hard? It's the least you could do given such a misleading title.