I suspect the important thing to notice is that there’s a real and persistent underlying phenomenon: the one-way passing of time, and an arbitrary and potentially large number of ways in which we humans can represent the time vector. But these aren’t the same thing.
For example, I can argue that elephants don’t “really” exist because I can choose to define elephants in a variety of ways and QED that “proves” that there’s no such thing as an objective elephant. The argument, of course, is spurious because it confuses signifier with signified.
Time does have an objective existence regardless of what metrics we choose to measure it by, otherwise the trivial example of relativity cited near the beginning of your article (the two brothers ageing at fractionally different rates due to their persistent difference in altitude) couldn’t happen. The world seems full of books written by those whose pseudo-philosophical ramblings are based on fundamental misunderstandings of ontology; it would appear you ended up reading one of them.