I'm going to go out on a limb here and guess that you're an internet cafe, and that's why this is professional.
LAN games are usually designed to run on a LAN. You've set up your VPN using internetworking techniques, and to put it simply, the game treats this much the same way as the internet in general. The broadcasts it needs, and any non-IP protocols it might want to use, cannot cross the VPN link because they are not routeable. This is by design. They tend to rely on broadcasts (and, for older ones, things like IPX/SPX, which is not IP at all), and a lot of the reason for having separate subnets in the first place (as you have done; each side of your VPN is a different subnet) is to prevent this traffic from crossing certain boundaries.
At risk of greatly increasing your broadcast domains (this negatively impacts scalability), you should set up a layer 2 bridge instead of a routed VPN. Your hardware might support this or it might not, but it is the correct solution. This type of connection between two otherwise separate networks typically uses a protocol such as L2TP, and relays pretty much all the traffic (IP or otherwise, broadcast or unicast) that exists on the wire at one site to the wire at another site. In this way, instead of being two separate connected networks, the networks appear to be one LAN for all intents and purposes.
If you do this and you have a lot of hosts with a lot of broadcast traffic you don't care about (such as Windows NetBIOS stuff), you should consider using a firewall in addition to a layer 2 bridge to drop some of it. This is a non-security application of a firewall, but is useful to limit the amount of spurious broadcast traffic, thereby limiting the impact of large broadcast domains).