Your Java installation is fine (as witnessed by this popup).
It's the engine server (server.exe) that is exiting.
I checked with a fresh UPPAAL installation on a unplugged Windows 10 and it shows the same symptoms, so it is probably proxy-related :-(
Could you please try without proxy?
You can also try running bin-Windows\server.exe directly from a command line (Start -> Run -> cmd.exe -> cd uppaal-4.1.26-2\bin-Windows) and paste the output here.
Best regards,
Marius