This does not seem to be a standard function.
To see if a machine runs a specific program you need to scan the processes on that computer, but you don't have access to this over the network.
What you could do is, you integrate a winsock control and write a very simple login routine to a kind of server which can run on one of the network computers. This server will then always reflect the number of running program instances and can report on which computer they run.