There indeed are some cartridge bottom brackets that have the cartridge insert from the non-drive side and the other cup from the drive side so this isn't unique. Another possibility is you have a cartridge like some of the older Shimanos that have both threaded cups removable and yours just has the non-drive side cup pressed onto the cartridge. And, yes English (by far the most common these days) threaded bottom bracket shells have left-handed threads on the drive side.

In any event, install it and ride.