Yes there is such thing as luck in chess. If you see the best move then yes. If you are too blind to see the best move, then blame your luck.
"Seeing the best move" or not is the very definition of skill (or lack thereof), not luck. Being "too blind" = lack of skill. Any decision made that has an element of skill in terms of game design is a skill-based endeavor, and a lack of skill or an element of uncertainty due to lack of knowledge is not luck. Uncertain outcomes do not just translate to "luck". Making guesses and getting an uncertain outcome from one of both players' decisions is an expression of their skill levels and to the degree that they fail, that displays a lack of skill, not some perception of "luck" rushing in to fill some void. If you make a guess in Trivial Pursuit on the question "What French leader ended his life on Saint Helena?" and you guess "Napoleon" rather than "Louis the XIV" because they are the only two you remember, that is skill, knowing the two leaders in the first place is an expression of skill (knowledge), and having some vague notion that Louis the XIV probably did not die in exile on an island is an expression of skill. Even if you "randomly" guess between the two and cannot articulate why, it is not actually random, your intuition has a basis, unless you actually flip a coin and introduce a randomized element.
The idea of luck you are talking about is the broadest definition, and is subjective. In game design, subjective perception of luck in not useful. Only completely randomized game elements are "luck", within the construct of a game's design and function. Luck that you experience externally (like eating a bad burrito, or getting a bad pairing in a tournament...tournaments rules also not being a part of chess, but added on top) in not luck *in* the game of chess you are playing.
Of course, this is an interpretation, but the difference is that one side's interpretation is based on some smattering of actuarial sciences/statistics, and the other is based on college level game design courses from Wharton and UCSCE.
Yes there is such thing as luck in chess. If you see the best move then yes. If you are too blind to see the best move, then blame your luck.