They may be Shimano SPD "knock-offs" but that doesn't mean SPD cleats will work. You really need to try to match the pedals with the same brand cleats. Shimano mountain bike shoes will probably work if you have the matching cleats. This type of pedal is not very expensive and it may make sense to start with new pedals, cleats, and shoes.
It would be strange to have mountain bike pedals/cleats, because it is a specialized road/urban bike.
There's a lot of road bikes with "SPD" or MTB type pedals and shoes. As others said, they work fine for those that use them and have advantages and disadvantages compared to "real" road pedals and shoes.
Look closely at the pedal and post any numbers or letters you see. It could help determine if they're directly compatible with Shimano SPD cleats (and the Wellgo equivalent), or if they're slightly different.