All depends on which distribution you run on the Raspberry Pi and what program you want to run on the other machine. It's also important to know what operating system that machine runs.
If it's a X11 program running on a Linux/Unix box then you should be able to log into that other machine and run your program there.
ssh user@machine -X -e /path/to/program/on/other/machine
You can also configure the user account
user on then other machine to only be able to run the program
machine. In that way you will increase the security a bit. As it wasn't part of the question, I will not try to answer how to set up secure kiosk.
If it's a MS Windows machine, it will be a bit more complicated I guess. But as I don't know how to use this on a Windows machine, some other will have to tell you how to do this.