How does longer length of optical path in binoculars increase its magnifying power?

Your question implies that you assume there are no other changes to the design besides the prisms. This is not the case. With these type of binoculars you are able to use an objective lens with a longer focal length (equivalent to the sum of the three segments). Longer focal length lenses can be larger in diameter resulting in a larger aperture. The binoculars thus capture more light from the object you are viewing. The more light, the better the resolution of the object (the more detail you can discern). The eyepieces can then be chosen to give more magnification with the same resolution as ordinary binoculars without a prism but this isn't always a good idea. Binoculars are hand-held and so too much magnification can result in a "shaky" image. Instead, having the same magnification with a sharper and brighter image is usually preferred.