TL;DR: Is there a safe way to play games over the network with an old computer with an old OS?

My son (5yo) really likes base-building games and we would like to play together.

Finding coop games we both like and can play on one computer is tough, let alone RTS games, so I was wondering if I could play with my own pc and an old computer over a local network, which allows a large library of (mostly old) games to play together. Games need to find each other over the network, and I will need a way to transfer files.

My plan was to use my own computer and an old laptop he can call his own and play on.

Connecting an old Windows 7 (EOL 2020) to the home network and internet seems like a bad idea however, so I was planning to disconnect my pc from the home network (cable and wifi), and then connect it directly to the old machine so they can only see each other.

I was wondering if this is a bad idea, perhaps I'm missing something?
(Lingering malware on old device? Or issues when reconnecting to a home network and internet later?)

Perhaps there is a better way altogether?
(e.g. don't disconnect but use whitelist firewalls, subnets, VMs, or ... something else.)

I have some knowledge of setting up networks but please assume I'm a noob.
(becoming a dad seems to have turned my brain into mush)

Strangely I didn't find any related questions, I thought this would be a common scenario.
I pondered asking on gaming.stackexchange.com , but that seems to have more focus on specific games themselves, and my questions are more about safe networking.

The old laptop needs some specific drivers and will just not work properly on Windows 8 or 10. I was happy the recovery still produced a working OS. Also sometimes things just work better on an old OS. So assume the OS will not change.