Wanna give a source for your definition? I have found others that disagree with your main sticking point and are more concise. I also play P2W games regularly.
"“Pay To Win” is defined as games in which you get an advantage in the game if you spend real money on items, weapons or features and are thus clearly superior to other players.
Most of the time, such games are free-to-play, making it very easy to get started in the game."
“Games that let you buy better gear or allow you to make better items then everyone else at a faster rate and then makes the game largely unbalanced even for people who have skill in the game without paying.”
“P2W is used in gaming with the meaning “Pay to Win,” to refer to games that allow players to purchase items or abilities (e.g., more powerful weapons, additional health points) that give them an advantage in the game, either over other players or NPC’s”
This is a blatant falsehood.