I've played in Nintendo Switch. Yes, it's portable. Can carry wherever you go and connect with a television and play with friends. Of Course, there's playstation 5. Xbox, etc.
You could buy a gaming laptop or desktop for your kid. If they have steam account, they can pretty much download and play the game they want.
Some of these options are pricey. It depends on your budget what you want to buy for your kid.
As your kid is just entering teenage years, you could go for a switch or Playstation or Xbox. There's PSP, playstation portable.
I'm not that much into games. The only game I play more is Chess. But you asked for options. These are some I can think of.