Spud is an executable that runs on your operating system like a simple window that's animated and chromakeyed. The Arm window captures the exact position of your cursor as it moves over it, and the Tablet window just mimicks whatever animation the Arm is doing. That's why the author recommends you put the Arm straight underneath your software's window so it captures your movements as you're drawing.
If your drawing monitor works as an extra screen on your PC, you just have to follow the instructions in the Readme. If it's more like a tablet that's standalone and gets recorded through a capture device like Elgato, it might prove a bit more complex, since Elgato mostly just renders whatever video signal passes through it, unlike OBS who can target executables, screens, windows, and the likes.