In a comment expanding on the question, you state,
I'm looking for a method that is kind of concise and closes the matter immediately rather than the chain of "why's" that I know I plagued my parents with when their answer was just straight up "no because we said so".
Please read this in the spirit it's given, because it sounds rough.
There is no better way to shut down your child's "whys" than with an authoritarian answer ("Because I said so"/"the makers of this video rate it PG13/whatever, and you're only seven"), unless it's to offer them something they'd rather do instead ("No, you can't play this game, but how about we go to the store and pick out a new game for you?"), which only postpones the issue. That's why your parents and mine and so many others resort to answering "Why?" that way. Which is not very satisfactory to a kid.
So, to answer your precise question, pick an authoritarian answer. If they ask "why" ad nauseam after you've warned them to stop, they've earned a time out.
Note, kids who are secure in your love for them will ask why anyway, because they actually want to know why they can't do something they want to do.
I propose something I believe is better for the long run: just explain why they actually can't play the game. If you consistently give them reasonable answers with your refusals, they will learn that you actually have a decent reason for saying no, and might not keep asking why. Or not.
This has two benefits: it treats the child as though their feelings and desires matter a lot to you, and it makes you examine your own reasons to deny them, helping you to avoid knee-jerk "No"s.
An example: My kids ask me if they can jump off the shed roof. To answer this honestly, I would say,
No, you can't, because I'm afraid you might hurt yourself.
It becomes clear to me that my fear is what I'm treating as most important to me. So I reconsider, weigh the risks, and say, "Ok, sure, but you have to go off sitting down on the edge of the roof (decreasing the actual terminal velocity, and therefore the risk of injury.)
I would recommend, then, that you figure out the reason you don't want your child to do something and answer all the whys yourself before they ask you next time. Then just tell them the truth.
This actually happened. Of six kids playing together, only one got hurt, and that was because she fell out of the tree used to climb to the shed roof. It wasn't serious, and I was able to fix it.