Think of Royal Server as a gateway to your infrastructure. As long as the machine you're installing Royal Server on can reach the actual servers you want to manage through Royal TS/X, that single Royal Server instance is enough.
If you run multiple environments that can't reach each other (network-wise) you'll need one Royal Server instance for each of those environments.
Example 1 (single environment):
You manage a company's IT infrastructure which operates from a single site using only one network subnet.
In this case a single Royal Server instance is enough. Since all of the servers you want to manage are in the same network, installing a Royal Server instance in that subnet will allow you to reach all of your company's servers.
Example 2 (multiple environments):
You manage a large company's IT infrastructure which operates from multiple sites (locations) using multiple network subnets.
In this case you need multiple Royal Server instances, one for each of the network subnets on which your company is running it's servers. Note though that you don't need to install Royal Server on each of the servers you want to manage. It's enough to install one instance per network subnet as long as the machine running Royal Server can reach the servers within that subnet.