Those outlets existed because pre-NEMA there were competing parallel and tandem bladed plugs/sockets [1]. The plugs you saw were probably like examples 2 & 3 in that link. The parallel configuration became NEMA 5-15P and the tandem became NEMA 2-15P.

The NEMA 6 series is wider than the 5 series and the 6-15P probably won't fit in those old outlets, but the NEMA 2-15P would. . . if you could find one.

1. https://plugsocketmuseum.nl/NorthAm2.html