Although a lot more money was spent creating the American version of the scare tape, it doesn't have the resonances that the original does.
Mainly because the original is steeped in cultural signposts from Japanese culture which include myths, fairy tales and Shintoism.
Sadako herself is a form of Kappa, or water demon. Her equivalent in western mythology would be the Wilis, who lead people to doom. They were made famous in the ballet, Giselle.
In both the Japanese and European version of this demon, the power of their hair is focused upon. In Japanese horror tales, the demons are frequently shown with wild hair, covering their faces. In western culture, hair is a symbol of beauty. But in the case of the Wilis, it is beauty gone to waste or rot. In the ballet, the dancers cannot have hair flying in their faces, but instead the veil is used as a substitute.
Back to the Sadako video, the "music" playing in the background is extremely significant. It is that of a flute, played off key as if the musician was distressed. It is a form of blasphemy against Shinto ritual music which often includes the flute. This music is often performed at shrines. But since Sadako herself was never given a proper burial, her music is understandably twisted. Interestingly, shinto music is performed by unmarried women, relatives of the shinto priest. Which brings back echoes of the Kappa/Wili myths.
The people in "mourning" and the man in the veil, also seem to symbolize the mourners that Sadako never had. But instead of lamenting her, they appear tortured. As her due as a demon, she unleashes her everlasting rage against them. So they crawl in pain.
In essence, Sadako is telling the viewer that her story, her life, and her death ground is something that will never be purified. Her curse will never stop.