Yes, outputting a diffirent voltage for each button could be what they use.
If this is the case, you should be able to just measure the voltage with your multimeter when you press a button.
But, it could also be a serial connection on wich information about the button pressed is sent digitally, one bit afther another. If this is the case then it gets more complicating. First you would need to figure out the protocol (How is the data formatted, how fast, ....) and if you want to manipulate this kind of connection yourself you'll need a microcontroller.