Advantage does not equal win.
If that quoted couple of lines is meaningless, you may want to look at other ways to interpret it.
actually, pay-to-win is referring to paying for an advantage in the game. It does not require an actual end-game win condition. For example, a multiplayer FPS may have certain weapons that can only be bought with real money, and are overpowered. In a match-based multiplayer game, there is no real "beating the game", per se. You could win a match, but there will always be another one and hence no real end-game. However, if you pay for an advantage over your peers, all else being equal, that is "pay-to-win".
Or we could go with Planetside 2 as our FPS example, as the world never resets, so while a faction may have an advantage over another to the point of owning the entire map except for the gates, this can always be reversed. However, there are certain weapons that can be unlocked for an advantage using money. Even though you cannot "win" according to your definition, buying these weapons with money is a pay-to-win element.