Good news! I've managed to replicate the issue. It's been fixed in version 1.1, which is now available for download. The game should now work fine even when blocked by that particular firewall.
The reason for the crash was simple. The game never tries to connect to the internet. It does, however, attempt to connect to a local RPC server, as explained here. Your firewall blocked it.
The reason why I was unable to replicate the issue is that blocking connection to 127.0.0.1 (localhost) is a very unusual thing to do, and all the firewall programs I've tried (including Windows Defender) simply don't allow you to do that.
You have previously never experienced such an issue with a Ren'Py game because none of them supported Discord Rich Presence. Honey Twigs: Winter Memories does.
Given how you took your time to submit such a detailed bug report, I felt it was only fair for me to respond with an equally detailed explanation.
Thank you for your help, and I hope you have a good day.