Let me throw this out at you. I was using this example as a way to explain to a layperson how you profit in poker, and I think it also illustrates the skill/chance issue quite well . . . .
Let's play a game. I have a six sided die, and we will gamble on the outcome. Now can we not all agree that it is completely chance what the result of the roll will be? Definitely we are playing a game of chance.
Now, I tell you "you pay me a dollar per roll, and if your number comes up, I'll pay you $5". You agree.
I have out played you, as long term I will win a dollar every six rolls. I have used the odds to my advantage and made the correct mathematical decision, and my long term results will show a profit. But we are still playing a game of chance.
Now, instead of agreeing to my terms, you counter with "No, if my number comes up, you pay me $7" and I agree.
Now you have outplayed me. Long term you will make a dollar every six rolls. You have made the correct mathematical play, and your long term results will be profitable. But we are still playing a game of chance.
This is what we do in poker, we make decisions based on the long term expectations of a particular play, but the result still holds that element of chance. So while we are using a skill to be profitable in the long term, the element of chance is not and cannot be negated.