Do I understand correctly that in your opinion it was not the software that I used, but that someone monitored and copied my private key and initiated the stealing transaction outside from my computer? Would the details of the transfer on Blockchain help to diagnose what actually happened?
Correct. Electron Cash has been in use for months now... I'm not aware of ANY instances where people have had coins stolen due to something that a "legit" version of ElectronCash has done.
Any loss is from users having either installed a "fake" version... or having had malware/keyloggers or whatever on their computer... and their private keys/seeds were compromised.
Maybe try doing a Google search for the address that your coins were sent to... see it it pops up in any other threads regarding stolen coins.