I'm not aware of any way to remotely check if a program is running on another computer. Other than running some sort of script/program on the networked computer and have it check and relay the info to the computer with the mirc script.
It wouldn't be too hard to make a python script or a simple C# program to check if either of those programs are running and write that info to a file. Then use a script to read that file and check if either are running. But that's getting away from mirc. Though if you had mirc on both computers it'd be possible to have a script on each computer that communicates between each other.
