Quoted from spfxted:All this stuff is possible. Not sure they would make a custom game. They would usually just alter something existing.
Thanks guys for trying to identify this game, it would be great if we could figure it out. As far as Columbia Pictures involvement in securing a pinball machine, you have to know that the budget for a Three Stooges short was tight. Therefore, the studio would of grabbed whatever was available at the lowest cost. The only modification they would make would be to cover over a company name (like they did to the Keeney's Red Hot in Three Little Pirates) or adapt the lights in the backbox to flash/etc.
So, based on what we have so far, it's a Bally made prior to 1942. Knowing Columbia, they would of bought a used machine. Using the "Pirates" short as an example, the short was filmed in 1946 and they used a '41 Keeney. Keep trying guys, the answer is out there!