Well, from my point of view there are two ways of doing it.
* Based on a PC or Raspberry Pi (Windows or Linux) - and then put together a small scoring application. Then you can have animations and sounds etc. It has been done already, just search for Skeeball in this forum.
* Full electric. It can be done with just relays (and some wiring), but going with an arduino would be very much more convenient. Pretty easy to setup in and outputs. I guess everything you need have already been done so just gather the information and copy paste.
When it comes to triggers I think most are using optical sensors, but a simple mechanical switch is doing it as well.
This makes me wanna build something my self...
