I say no and yes.
"No" because I am aware of what is good and what is bad in games or films. I do not adapt bad/evil logics/actions to my behavior and personality. I just am aware that those exist.
And "Yes" because not all children are like the way I was that learn and absorb only good things. Most children these past decade absorb anything from cussing to criminal behavior/logic. Parents/Guardians should be monitoring those children but they aren't thus contributing to the issue.
Yes game age matters, for example kids shouldn't be playing battle royals, this isn't ancient Rome where anyone could watch gladiator games, nor should they be playing gambling games on consels. Age ratings are here for a good reason.
It's for the best that governments are starting to crack down on some of the worst excesses of children being exposed to gambling elements in video games. I am much more moderate in my opinions that I don't think video games particularly cause violence. The communities for some games were already just not concerned with manners or whatnot, and that's what gets perpetuated. Violence comes from what is accessible, and America is particularly accessible about guns unfortunately.
That being said, you still should care about the age suggestions for games. Being proactive about what kids consume is important, even if kids will find it restrictive. It's the job of parents to bring up their kids well and to have some impulse control over what they consume (Even if we ourselves are shortsighted and impulsive over what we consume! *wink*.