A project claiming to offer digital immortality I think would need to offer at least one of two particular features to live up to that description. (A) It would have to directly augment the human body to extend its lifetime indefinitely or (B) it would need to emulate the target human in such a way as to provide extensional equality. Extensional equality [1] in this context I think would mean that for any given situation, the human and the emulator would need to behave equivalently. This automatically entails that it would need to have the same thoughts, contain the same memories, etc to provide the necessary context for its decision-making.
Neither (A) or (B) consider any ethical implications of course. I'm just musing off the top of my head. My point is that although I think eterni.me could still pan out to be a cool project, it falls short of achieving digital immortality.