Tell us about yourself!
So the wiring of the matrix really depends on the type of matrix display you have, The one used here has tristate LEDs, but I have recently changed to using a matrix based on the ws2812b LEDs, which are programmable. They only use one wire which makes it easier to connect up and also to control. As a start you could even just use large single LEDs.
I used a basic 2n2222 transistor, on of the most common transistors around. It is used because the arduino IO pins cant supply enough current to power the LEDs directly.
Thanks for the comment. Do you have the pull up and pull down resistors in place? Also enable the serial debug code and see what output that gives you. It should tell if you have a hit or not. Which should tell you if your issue is on the scoring side or the lights side.