This is true, especially in the context of EVE, but people like to confuse the issue so they can pretend they aren’t buying their edge with RL $$.
First off, you will get the crowd who will refer to theoretically ‘pure’ P2W - which is a PvP oriented game where the cash shop sells super-items, bound to character, available no other way in the game, against which a non-cash-shop player cannot possible win (Super Vorpal Sword of One-Hit Instant Death! Only $100!). Of course, there are virtually no games like this, and even then it’s not ‘pure’ P2W, because if someone else buys the same sword, then you are not guaranteed a win.
Then there are the games people often cry ‘P2W!’ about, which are in fact PvE games (Neverwinter, Star Trek Online), with minimal PvP. In general, since neither the in-game market nor 93% of game play is actually competitive, what you are really paying for is “P2-have-more-stuff, P2-look-cooler, P2-be-top-DPS in a PvE dungeon”. Also, there is generally a natural limit to what you can pay for… once you have dropped a couple hundred bucks on things there just isn’t much more you can add to your character.
Then there are games like EVE, which are actually “P2-adjust-the-odds-in-your-favor”. The wallet warriors who are desperately trying to convince themselves they aren’t buying wins will say “bu-bu-but the guy who pays could be AFK! He could be a noob! He could be asleep, and he will lose! So it’s not P2W see!”. But as you said, you have to assume two roughly equal players… one pays for an edge, one does not. Who wins?
EVE is directly competitive, in all aspects - resource gathering, material production, market trading, player PvP, even PvE farming. Because the market is ‘player driven’, all economic aspects (which is pretty much everything) are in competition against other players. Your effectiveness in this competition is directly driven by your ISK bankroll, your bling modules, your trained SP, the pilots in your stable, the number of accounts you can Omega, the ships you can afford, the alts you can bring to the action.
Every single aspect of EVE (except for personal player experience/skill at ‘playing the game’) is purchaseable, with no upper limit (except maxing all skills), and it all contributes to your competitive edge. EVE is actually, in my four decades of gaming experience, the most P2W game that has ever existed.
Worrying about the effect of extractor/injectors (as per the OP) is short-sighted at best, since it is merely the ‘icing on the cake’ of the EVE P2W model.
As an important side note: EVE is pretty much only successful because it is and always has been P2W. It is a competitive game, with real consequences to losing, where you can pay real $$ to make it less likely you will lose. Whether those dollars were spent on subbing for years so you can train your SP higher than someone who didn’t, or buying pre-trained pilots, or on RMT, or Plex, or more recently, injectors… you could always buy an edge with cash.
That is what has led to the whales in EVE, that is what has led to sloppy game design, and CCP devs deluding themselves into thinking they are selling in the “$1,000 Designer Japanese Jeans” market when they are actually closer to the “plastic guns, building blocks and train sets at Wal-Mart” market.