Thank you GlennD , your simple suggestion solved the problem.
Why should developers allow users to install Hamachi in a different directory if doing it will cause known issues? It doesn't make much sense to me...
Anyway, now I can ping other clients in the network, but I'm getting the Inbound Traffic Blocked warning when clicking on Diagnose on one of the connected clients (right click -> Diagnose).
Does this warning cause any problem when communicating with others?
I've tried unchecking "Hamachi" in the list of protected networks (in Firewall advanced settings), added an inbound rule and allowed the Hamachi application. But the warning is still there.