I read the posted article, and as I suspected, this is a content-free theory. An instant in time exists in the limit of zero interval; you can take measurements over ever decreasing intervals, and extrapolate to zero interval. In effect, that's what most physical measurements do, implicitly or explicitly. One could similarly argue that a single point location does not exist, since all real objects have finite length.
Oddly enough, he dosn't seem to have a problem with saying a precisely defined point exists on a spatial coordinate.