Finally, the audio amplifier arrived in the mail! So, soldered all the connections, plugged in the power to Raspberry Pi's GPIO pins and off we go! So, everything in this project (display, sound, lights) are powered from the RPi.

Designed the removable panel to allow the amplifier to be mounted and you can adjust the volume using a small knob.

And this is how the back of the arcade machine looks like now in the final design.

Here's the full video of the completed project.