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

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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.  

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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.

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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.