That would be a true description of any pay-to-win game — if you just buy everything available to be purchased, then you’re playing on a level-playing field.
But using this description, then the only truly pay-to-win game would be one where the win condition is literally an auction selling a “you win!” token.
I'd go around money advantage being way too significant and the money cap way too high or non-existent. Otherwise every game is kind of pay to win as getting your hands on one more chess book, or getting a better tennis racket gets you an advantage.
While mtg is not cheap, I would say that only older cards get crazy expensive and sometimes are straight out overpowered.
But using this description, then the only truly pay-to-win game would be one where the win condition is literally an auction selling a “you win!” token.