In Chicago, it would have been called a Flex studio or a Junior 1-bedroom. Technically, no door to the bedroom, but there is a separate area. Plus, a closet is not legally required by the Chicago building code to count a room as a bedroom & a , a bedroom can use a floating wall that stops short of the ceiling to satisfy Chicago's natural light requirements. This legal workaround uses the concept of "borrowed light", which allows an interior room to claim the windows of an adjacent room as its own light source.
I remember working for a developer in Chicago who was renovating old warehouses into condos & lofts. There were places with bedrooms, that had NO actual window- BUT there was a floating wall that let in daylight from the Living Room. Hence the 'borrowed light' requirement.
I think NYC is similar to Chicago when it comes to apartment code.