I wouldn't describe chess as a lucky game, and I wouldn't compare it to poker, but I wouldn't say your performance at a tournament is completely under your control.
Anyway, it's not a new idea.
"A good player is always lucky" - Capablanca
"The player who plays best in a tournament never wins first. He finishes second behind the guy with the most luck." - Tartakower
The rules describe a game with no luck.
Imperfect players introduce at least a small element of chance.
Yes, humans are imperfect, they make mistakes. For example, one can make mistakes in simple mathematics if he makes the calculations by himself. But you can't say there's luck in mathematics... can you?
"Why didn't you score well in that math test?" "Oh, i was unlucky... We got questions from the part of the book i hadn't studied, and made some mistakes in the questions i had studied, too" "Ah, don't worry son, next time your luck will turn around" :D lol
Im separating the two.
So I would say a human's performance in math can be fortunate or unfortunate.
Performance can even be very arbitrary. For example on a math test, it's not whether or not you can solve a problem, it's whether you can solve it in that time frame.