OK here are all my thoughts on this. As an overall comment, information on this era of Bally's games is scant, contradictory, and hard to follow. There is a list out there of Bally project numbers in numerical order, but they didn't always seem to get released in anything close to numerical order...or maybe some of the release date info is wrong... or the fact that they reused game names from time to time confuses things.
I believe that the game we see from the side is not the same game that we see in closeup of the backglass and playfield. The closeup shots were absolutely filmed in a different location, and therefore would not have to be the same game, and I'm pretty sure they're not. But the backglass and playfield match, and are definitely from a Bally game. The cabinet wouldn't have to be a Bally game, but I'm pretty sure it is.
At the head of this thread, look at the closeup pictures, especially the one of the backglass. To the right side you do not see a white wall an inch or two away, you see open space, and carpet, and probably a tall potted plant! In the distance to the left in the backglass shot you see a chair, or possibly another arcade game, plus what looks like more large plants. This is in an office or hotel lobby or a fancy arcade or something, not on a "jail" set in a studio. They went on location somewhere to film the closeups, it's not the harsh lighting conditions of the jail set.
The tall backglass dates the game as no earlier than very very late 1938, more likely 1939. The non-script Bally logo on the playfield and the spring rebounds on the sides put it no later than maybe mid-1940. So in all likelihood that's a 1939-ish game. But those games had simple wooden side rails and shallow backboxes with flat bottoms. The cabinet pictured in the film has a deeper backbox with a sloping bottom, and side rails that have a vertical component along the cabinet. For instance see Dark Horse from November 1940:
But by November 1940 they were using the script Bally logo and pretty much not using the spring side rails on the playfield. So I'm all the more convinced that the cabinet is a different game. The three leg bolts would probably help nail it more closely, if there were more info out there about Pre-war bally games.
Try as I might to play with that image as seen from the side in PhotoShop, I can not bring out enough more detail to make an ID (it's not like in the movies where you just say "enhance!") But it sure looks to me like a game that has an arc of large lit areas across the top (which was very common) rather than the more grid-like arrangement pictured in the closeups.
Google Books' collection of Billboard Magazine scans does not go back far enough to be useful here. I think we're going to need to find the so-far-unknown pre-war Bally ephemera collector to ever sort this out, unless someone happens upon one of these two games in a barn somewhere and then stumbles across this thread. Which is also unlikely, given that LaGuardia and his ilk smashed a lot of these games and dumped them in various harbors around this time.