After wrestling with this issue for couple of days, I finally got it working.
uninstalling / reinstalling does not resolve the issue in itself
I noticed in the middle of az uninstall/reinstall process that I had 3 copies of the Hamachi network adapter. It only happened once though.
I then got better results in diganostics, the only problem shown were offline peers.
But while peer was online, got that annoying VPN error message, and ping was still unsuccessful.
I was struggling with it for couple of days before discovering that my bluetooth adapter also created some sort of VPN I haven't noticed...
Now, when diagnosing the peer, I still got an "inbound traffic blocked" message for some reason, but the Diagnostic Tool only shows offline peers as errors, ping is finally OK, and the Hamachi network itself seems to be working 
So I think the solution should be
- Before installing, disable any other device that might be using a VPN sort of (that was a bluetooth device in my case, and there was a VPN option in my network card's setting that I also disabled)
- If you are reinstalling, check for and remove any duplicates of hamachi adapter manually, then uninstall / reinstall hamachi
- add hamachi as an exception to your firewall, or open the used ports (I only added Hamachi to Windows Firewall exceptions, as it's finally working, I don't mind changing the router settings)
I hope it helps for some of you
