At some level of abstraction defining and making equivalent “games” as rules that guide play draws a thing Americans are familiar with called 1040 into the corral of games. Because all you have done at that level of abstraction is begged the question “what is X?” Aaannnd… you now have two X to deal with. What are rules, and what is play?
And, yes, play how you want to play, and yes, it’s difficult to differentiate at the edges what genre of game you playing. And yes, that’s ultimately not meaningful.
And yes, it is useful, within the context of table top roll-playing games, to recognize that the relationship between rules text and player is different from the relationship between rules text and player in professional sport. For that matter, that relationship in professional sport is different from it in other sport iterations. When you are a Detroit Lion, and you go to work playing football your relationship to the rules is different from when you take a few friends into the back yard and play football while the chili is simmering.
In TTRPG the rules are fundamentally a social compact about how the players are going to treat each other, through imaginary characters in an imaginary space. This is a game, and rules of the game cannot adequately address all the ways people are going to be people with each other, especially when all the people are pretending to be people other than themselves but really cannot ever stop being themselves.
And that’s when rulings come into play. They are going to happen at you TTRPG table. Someone will misremember (or totally forget) a rule during play, the play will go, and in a similar circumstance you’ll do that rule-adjacent thing again, and then whoa, it’s now a house rule.
And all this is non-controversial (ha!). But the thing about this rules, game text, game play, table play folderol is mainly to push game designers to think harder about what they’re trying to accomplish with play as distinct from how they’re trying to model cause&effect.