I went through my handful of pics showing some of my 35X/36X stuff and here's the best picture I have of the back plates for a 36X needle bearing engine. Hard to tell here, but yes, the outside diameter of the back plate is less than the inside diameter of the case, so there is "slop" when the back plate is in place sans screws. (I used to wrap the NB back plate with flexible 1/16" balsa to fill the void.) Also note the long protrusion that was cast on that was to be drilled-out and a pressure fitting installed if case pressure was desired.
The later back plates for the 36X BB was a closer fit inside the case and lacked the protrusion to the rear for the pressure fitting.
I suspect you have a back plate for a needle bearing 36X.