So those are some tentative thoughts; I was wondering what other people might think? How do you play now? What do you prefer? Do you think it makes a difference, or is this an arbitrary distinction without a difference?
I'm going to zoom out a bit...
Broadly, being skilled is being able to do a thing quickly, well, and with relatively low effort. But, skills are not entirely transferable. Being a skilled carpenter does not make you a skilled cellist. So, "skilled play" as Gygax wrote about it, is really "skilled
Gygaxian play" - approaching the game as Gygax seems to have preferred, and using a particular set of skills and knowledge his games engendered and required.
What counts as "skilled play" though, is going to change from game to game. If you bring skilled Gygaxian play to my Fate-based pulp-action game, you are not going to succeed often, and are apt to have a pretty unfulfilling rpg experience.
More broadly, then, skilled play is knowing and using the rules and genre of the particular game, and being able to lean into them to enhance play for yourself and the table. "Skilled play" is defined relative to the rule set, genre, and goals of play.
In Gygaxian 1e, skilled play is constant explicit pixel-bitching searches and prodding each square of a corridor with a 10' pole to set off traps before you get there. In 5e, the skilled play is setting up your character with a 23 passive investigation skill so that they're bloody Sherlock Holmes.
So, returning to the OP then, we reveal that while the dichotomy between skilled Gygaxian play and role play may make some sense, skilled play
in general is only opposite skilled play in some games/genres, but not in all.