Is there a way to run resource monitor (resmon.exe) without administrator privileges?

As Resource Monitor displays live statistics on network-traffic and open files and tasks of ALL users, it needs access to that Information. This access requires admin access.

So, the answer is: no it's not possible for the Process to not have admin rights.

What you CAN do however, is to set up a (sheduled) task, that the user is allowed to start. that task in turn, could start the res mon. So the user can start the ressource monitor without requireing adminrights, and he also can't do other stuff with the rights (apart from the options resmon.exe gives him, like stopping/starting tasks ...)

Hope this helps you.