Hamachi creates a VPN between you and other people over the internet, kind of like having them on your LAN.
Yes you can play KaM Remake over it, although it's probably easier just to join one of our servers. However you could get lower pings through Hamachi if you don't live near any of the servers.
To play over Hamachi:
1. Connect everyone on the same Hamachi network
2. On the host computer click Create Server and then Create Local Server
3. On the other players' computers, click "Find Server by IP" and type in the host's Hamachi IP (I think you can right click and go "copy IP" in Hamachi) then click connect
4. If that doesn't work try disabling the firewall on the host or make an exception to allow KaM Remake to accept incoming connections (which is often blocked by default). Also make sure you all have the same port number entered, the default of 56789 will do fine.
Let us know how it goes

Cheers,
Lewin.