Welcome aboard, Gruntchovski.

This is certainly an unusual build concept.
The gumball mechanism I'd imagine would be the trickiest part.
For the gumball mech, you could use a servo/actuator/motor attached to a horizontal dowel with a slightly-larger than gumball hole drilled partway thru the side.

When the hole is facing up, one gumball falls into the hole.
When it's time to dispense a gumball, the servo/actuator/motor turns the dowel far enough for the gumball to fall out, then it returns to the upright position.
You can use upper/lower limit switches to ensure the dowel rotates far enough in each direction.
If the servo/actuator/motor position is controlled by PWM, you'll need some sort of controller circuit.
If the servo/actuator/motor reverses direction when polarity is reversed you can wire it like this diagram, but using two solid-state relays controlled by the Pi in place of the DPDT rocker switch. (related thread
here)

I'm not sure if this counts as an "Arcade" project either.
No worries. WannabeJoy's build
here wasn't an "arcade" project either, but it was fun and educational.

Scott