its not possible with vSphere ESXi. Its an enterprise Hypervisor which doesn't have UI (console) which support third party user software's like games.
For this you can go for VMware Workstation which is installed on a Linux or Windows Host OS.
1. Install Linux/Windows on server.
2. Install VMware work station.
3. Create VMs.
4. Install Game.
In this case you can play game on this server at console . At the same time others can access their VMs.
More details on workstation available here. http://www.vmware.com/products/workstation/