NO, A single VPS Server can't handle so many games as they eat too much CPU.Better go for a dedicated server & increase your budget as you need a powerful CPU to host so many games on a single server.
What is VPS Server?
VPS Server is a virtual private server, is a virtual machine sold as a service by an Internet hosting service. A VPS runs its own copy of an operating system, and customers may have superuser-level access to that operating system instance, so they can install almost any software that runs on that OS.