Auto-translated
A static address is an address that does not change when you reconnect.
A dynamic address is one where a different address is assigned each time you reconnect.
IP address.
192.168.xxx.xxx and 10.xxx.xxx.xxx are local (gray) addresses. If the router didn't allow it, it wouldn't work through Hamachi either.
VPN - Virtual Private Network. Hamachi creates a virtual network connection and uses it to organize a virtual local network (which, of course, does not have a gateway for accessing the internet). I haven't looked at how TeamViewer works, but I think it's similar. In my case, there is a VPN connection that combines the necessary computers into a local network without a gateway (i.e., without access to the internet through the VPN), and there is a network connection to the internet (through a router, i.e., also with its own local network). Heroes 3 only sees the router's local network, but it refuses to see the VPN's local network. The question is
specifically how to
make the game (Heroes 3) see the VPN connection's local network?