A human action is behind flipping a coin, selecting a card from a deck, rolling a dice, picking a number out of a hat, etc. too
the results of those things are based on chance not the human action which is based on skill, focus, ability, etc.. I think you already know this though but still felt the need to make your statement for the sake of argument. I expect nothing less from a member of this community.
I should be clear that my position is not an opinion. It is a fact, statistically speaking, that luck/randomness/entropy/chance/whatever your personal preference of verbiage is a part of any human process (be it hitting a baseball, performing surgery, drawing a circle, selecting stocks, etc.).
If you (correctly) recognize that all of my examples are based on chance, then something that may help you understand is to think about if a player selects his moves based on said chance. So all available moves are put in a deck, randomly shuffled, and the player plays whatever the top card is. In any given position, it would not be that rare to see the player choose the "correct" move in the position, based solely on the outcome of the shuffle. Using this strategy over the course of a game though, the probability of repeated "correct" selections decreases exponentially by the number of trials.
Hence chess is a game of skill (a skilled player plays "correct" moves at a reliably higher rate than chance) with elements of luck intertwined (the basis for their selection need not be based on anything concrete) just like anything else.
The higher an activity trends toward the skill side of the luck-to-skill spectrum, the lower the number of trials needed to ascertain ability vs. luck. Since chess is pretty high up there on the skill spectrum I'd say, it would be obvious within 10 moves that I am far worse than a GM for instance. But the point is that it is on a spectrum and not a boolean.
There is nothing random about that.
The design of chess, which you put great stock in, presumes that players will look at the board before they move. Beginners look without comprehension and make moves that appear random.
Maybe you are right that is is not random. Maybe you can explain the thought process behind dropping pieces willy nilly and resigning just before you win on time. Maybe you can explain the logic of moves that appear to be random chance to chessplayers who see elementary relationships between pieces.
Everyone suffers blindness now and then. Their adversaries benefit from the failure of perception. That’s a luck break. Kramnik missed a mate in one, once, in thousands of games. Many GMs have. I’ve missed a mate in one hundreds of times. Beginners often miss a mate in one twenty times in a single game.
How can we claim that the opponent of such a player is winning on the basis of skill?
Capitalizing on an opponents mistakes or lack of skill is not random chance; Failing to see a mate in one is a lack of skill, not random chance.
I prefer random chance to luck, as anyone can claim anything is luck. It is a nebulous term.