This is quite interesting. Unfortunately, there are no recent studies to back some of the claims made. Also, the correlation observed in the animal kingdom arose from the comparison of animals of different species, not the same species. Humans are of the same species.
Some of the arguments about height having some correlations with cancer could have been plausible assuming our body maintains the same cell division rate throughout our life cycle.
RE: The Intriguing Correlation Between Height and Lifespan