There's no overload for GetProcesses()
on a remote machine, but if you're just looking for a particular process name, you could try the GetProcessesByName(string, string)
overload, which allows you to pass a machine name as the second parameter.
See MSDN for more information: https://msdn.microsoft.com/en-us/library/725c3z81(v=vs.110).aspx
Also, please note that you are not actually executing your command on a remote computer, but rather making a request to a remote computer. In order to do that, you would want to look into WCF (Windows Communication Foundation; start here: https://msdn.microsoft.com/en-us/library/ms731082%28v=vs.110%29.aspx). You could run a service on the remote computer and have a client on your local computer consume that service. The client might send a message like "Get me all the processes!" and the service would return a list of processes after running Process.GetProcesses()
on the remote machine.
If you're asking about a way to execute arbitrary code on a remote machine without any special tooling or libraries, there is none (or rather, there are at times but they're considered major security vulnerabilities and get patched when found).
Alternatively, it's possible to make use of the Remote Desktop Protocol (RDP) to do what you're trying to achieve. It's possible to make use of this programatically, but you might have a hard time limiting it to just one application.