I think the stigma with "real gamers" when they hear that someone only plays mobile games is that the "real Gamer" sees this person as part of the problems that have infected the industry. Let's face it us "real gamers" are not buying microtransactions, we aren't stuffing GTA with shark cards, we aren't Fortnite dancing, we aren actively and powerfully against that kind of thing. So when we see someone that says "Oh I only play a few games on the phone." It instantly triggers us like, "YOU!! You're one of the fuckers ruining everything for all of us!" Because if someone only plays mobile games then you know they are feeding that toxic ecosystem that inherently infects everything else.
So the attitude is toxic for sure, but what other defense do "real gamers" have. It's not like you are going to sit and have a conversation with this person as to why buying extra lives in candy crush is actively destroying gaming for everyone. Nobody would listen because the people playing mobile games don't actual care. To them there is no consideration about the money, or the quality of the piece of shit they are playing, they just want to get through level 397. As a result the only impact one might have on this person and in gaming as a whole is to shame the mobile player.
The thing is there is a right way and a wrong way of playing mobile games. People who put minecraft on their tablet so their kid will shut the fuck up while the adult eat dinner or whatever is fine. There is nothing wrong with minecraft on the mobile system because it's the same as the console in the fact that you buy it and you have minecraft whatever. It's an entirely different thing to give that same kid fortnight, or angry birds, or even candy crush, because everything about those games wants you to spend money, they exist for you to spend endless money on them and parents really should be educated on this becuase it's predatory and the kid isn't going to know any better, they just want the dinosaur skin or whatever, and the parent even with self control might buy it for a birthday or being well-behaved or whatever and that's wrong. Not because it's bad to buy a gift or reward the child but because the draw of sinking money into these games never ends. And by the time you catch yourself you've bought enough fucking skins, or extra turns, or whatever to outright pay for a Playstation 5 at scalper prices and you've nothing to show for it but a game that will never stop asking you for more money.