That's quite plausible. One reason, though, I blame Gen X here for surrendering their children isn't due to any special knowledge I have of how all of Gen X thinks, but is a matter of the numbers. Because Gen X are older than the Millennials, I assume Gen X have had more kids than the Millennials. And if those kids are hooked on the apps, their parents have effectively surrendered them to the big tech companies.
The problem you raise is that the parents' intention might have been otherwise. Maybe Gen X did fight valiantly against this tendency, but those parents just lost out to the more powerful, big tech environment. In that case, it would be unfair to blame the parents' weakness as the sole cause of this defeat. But we have to wonder whether the parents could have faught harder and demanded more from their children and from the government.
The slackers did grow up to be overprotective and pampering, which means they surrender to their children all the time. These overprotective parents aren't strict disciplinarians. And that's why I suspect we can still fairly speak of a parental surrender that flows from the defeated character of Gen X. That generation is overprotective because they don't believe much in any higher power of institution, and because they're bleeding heart liberal progressives.
Gen X tortured themselves (needlessly?) as teens, and they don't want to torture their children in turn. So they submit to their children and let them have their way. In effect, they cede the parental role to the big tech companies which train young people to consume.