This article seems inherently flawed in its assumption that a. the exponential growth of computing power will keep up, despite the numerous technical and physical boundaries imposed upon them, b. computational power will solve many of the unknown inner workings of the human body, and c. that being aware of, and understanding those inner workings allows us to modify the human body in such a way that we can 'rejuvinate' the system.
While I do feel that life expectancy of everyone below 40 is probably going to massively higher than historical life expecancies (disregarding systemic failures of society and outside influences), I don't foresee a future where everyone gets to live forever.
Moore's law has not been an exponential increase in technological capability in general. It has only been an exponential increase in one particular technology - more of the same. I see no evidence that the development of novel technology in general has sped up in any way.
While I do feel that life expectancy of everyone below 40 is probably going to massively higher than historical life expecancies (disregarding systemic failures of society and outside influences), I don't foresee a future where everyone gets to live forever.