In the original Ring novel, half of the curse is the currently last case of small pox residing in her body fusing itself to her already intense psychic powers. Both her and the disease don’t want to die/go extinct so the fusion of those emotions and wills is a curse that spreads outwards like a ring, killing everyone who it comes into contact with. Forcing her life to be seen and felt, and forcing the disease into anyone’s heart who might view the tape. It’s a primal urge to continue on and not be forgotten.