Okay, it sounds like your IP address did change after cloning your MAC. Are you using the same account user name for the game? It will not be DNS (that just resolves host names IE microsoft.com to an IP address) or a subnet mask.
I think I got your answer assuming your ISP uses DHCP to assign your public IP address which it sounds like it does based on your post.
First run ipconfig/all and copy down the MAC (physical address) address of your NIC card.
Then take that info and enable MAC cloning inside your router. Use the MAC address of your NIC card inside the settings of MAC cloning.
Then release renew your external interface (WAN) of your router. This should cause your ISP to give you another public IP address.
The IP address is leased to the MAC address that requests it. In this case I am sure he is using either the same router or NIC card. In either case the requesting MAC would be the same and the same IP address would be handed out until the lease expires.