That is definitely a manufacturing defect as this style does not exist under the Nema specification.
This "2-prong" plug and socket design, with two flat parallel
non-coplanar blades and slots, is used in most of North America and on the east coast of South America on lamps; consumer electronics such as clocks, radios, and battery chargers; and other
double insulated small appliances that don't require grounding (earthing).
All NEMA 1 devices are two-wire non-grounding devices (hot-neutral) rated for 125 V maximum.
If it makes you feel any better you can look at the cable for the text embedded into the wire - this would be the ( hot side ) narrow blade. you could also look at the end of the plug between the two blades for the text that is between the blades. when reading the text the narrow blade should be on the right side.
So go ahead and use a dremmel or some other toll such as a good pair of wire cutters to trim down one blade.
Note - the difference between a three blade and two blade plug is the two blade uses a internally grounded circuit in case of a short and the three blade is externally grounded. Normally the two blade design can be reversed as needed.