At first, I thought this was hilarious that I even managed to get this working, although after some tinkering, I think it works pretty well as an alternative to Gmail's default mail viewer. With enough tinkering, you can even get RSS feeds for most modern websites to work. I made a guide below.
Addendum 10/12/2024: You need TLS 1.1 and 1.2 enabled to be able to use secure connections and authentication. This quick-fix from Microsoft should fix it for you.
Thanks to @nonamed for pointing this out on the Discord server.
The first part is simple (if you have a phone, at least). To allow Live Mail to access your Gmail account, you need to create an app password for it. This isn't possible without enabling two-step verification with your phone.
Enable two-step verification with your phone number here
Create an app password here, and name it something so you can identify it.
After you complete this step, you need to go into your Gmail account and change some settings, shown below.
The last step is to sign-in to your Google account from Windows Live Mail (left). This is where you need to use the app password you made earlier.
After that, you need to properly configure your server settings using IMAP (right).
Incoming server address and port: imap.gmail.com:993
Outgoing server address and port: smtp.gmail.com:25
Make sure SSL authentication is checked.