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Did you wait about 30sec? The engine is RenPy and that means though you extracted the ZIP file their inner PY files are compressed too. The game needs them to wait for finishing self-extraction every launch before display the game window itself.

But probably themain  cause might be that your antivirus think it could be ransomware and pauses the execution at runtime without any notify. Because RenPy is able to alter lots of files in a short amount of time - and that makes the engine suspicious, not HHG in special but alle those VNs. Whitelist the game and you should be fine next launch. I have to do this for Acronis and AppCheck always.

And if it is not that, maybe another process consumes way too much CPU ressources (or has too high priority). Look into your Task-Manager and verify your system has enough capacities left.

The downloaded files are healthy for sure. TCP/IP overwatches download stream and correct issues automatically without ever telling you (except if you use UDP). Even if bits would get lost, the binary (EXE/DLL) shows an error message in 99,9% because of code is corrupt or cannot be interpreted. No error message means the app is downloaded fine as well as it fits your architecture (other apps must be the problem then).

If Dragodraki's suggestion doesn't help then try deleting the files and download the game again, a small hiccup in internet connection can cause some files to not download properly. then extract the files like normal to your desired location and run the application again