Do we have to install the tool on each machine?
That is how most of our customers use Test Studio, but no it is not absolutely required.
or can we install the tool on a server machine and have users access it simultaneously.
That is permissible, as long as the number of concurrent users does not exceed the number of licenses you have purchased, 5 in this case.
I am curious, how do you intend to use your 10 Run-Time licenses? This edition is meant to be installed on build servers, test agents, test only machines, scheduling server, execution server, etc. And just in case you don't already know this, you do not install full Test Studio and a Run-Time license on the same machine at the same time. Full Test Studio includes everything that you get with the Run-Time edition.
the Telerik team