The top of the windshield frame looks like it has holes for a roadster top/bracket, but no frame or other indication.
I believe that's what it is. (my Mom had one in '34, her friends called it a 'chummy roadster' with its rumble seat) Funny old slang...
Never a roadster, as others pointed out the obvious giveaways as the windshield and tops of the doors cut off. Plus 30-31 roadsters do not have the double bead at the beltline.
In other words, "just like a roadster, only different". Windshield/cowling completely different. Doors on a roadster roll into the cowl at front, are narrow along the top (no side windows) are shorter in length, rear upper valance (behind seat) is longer, trunk lid the same. There's no way a Cabriolet, sport coupe, or coupe could be confused with a roadster. Unless someone was 'confused'...or unaware/ignorant. There's a book....