Perhaps a better way to explain myself is by looking at what I'd consider a sign of how much skill is involved in a game: roughly speaking, how many different strata of players are there for a widely played game, where each stratum can beat the stratum below (let's say) 90% of the time? There's only one stratum for Candyland, and at most three (humanly speaking) for tic-tac-toe, but numerous strata for a game like tennis.

So we can think of luck-vs-skill also in the sense that tennis is more stratified than golf, because a few PGA players have a 10% or better chance of beating Tiger on a given weekend, and many PGA players have a 10% or better chance of beating one of those players, and a top amateur or college golfer has a 10% chance of beating one of those players, and so on down; while there seem to be more layers than that in tennis.

Now, high-stakes games can cause a selection bias wherein all lower strata will withdraw from a competition, but this doesn't change the components of skill and luck for that game; if you forced the withdrawing players to play for those high stakes, you'd see similar results as you'd see for low stakes (neglecting psychological effects of the fear of a bigger loss, but your analysis doesn't seem to incorporate these). The usual concepts of skill and luck are defined by what would happen if X played against Y; your analysis is about something else, which determines whether X plays in the first place. So please call it something else.