Thanks for the video, that makes what you are seeing more clear. You are seeing that Spine runs when you are online but not when offline. We've reproduced the problem so it seems we'll need to release an updated launcher. Sorry for the trouble! I'll post here when it's up.
FWIW, we've rewritten the launcher completely in v4. It's smarter and faster, allows you to choose language and version before launching, plus it looks really cool. 🙂
We've now updated the launcher downloads for all OSes to from version 3.8.82 to 3.8.97. If you download and reinstall Spine, you should be able to run offline as long as you have previously downloaded the update file for the version you are trying to start.