There's no paywall. There's also an accompanying slideshow. Most articles speculating about the future of human evolution are written without an understanding of the theory of cultural evolution - however this is not one of those articles.
The article paints a picture of longer-lived humans and more effort expended by them on meme propagation than gene propagation. These seem like extrapolations of current trends.
However, the paper's forecasts extend out to 2050 - a significant distance out - and in a zone where is challenging to make reliable forecasts.
My own perspective is that we will probably see a large explosion of artificial life significantly before then - which will have a big impact on the terrestrial ecosystem. Eventually this will turn the human world into a sideshow - the coming memetic takeover which I frequently speak of.
This is likely to be the real story of the next forty years. Life extension and reduced fertility of humans seems like a rather irrelevant by comparison - these things will have negligible socio-economic impact.
Indeed, they are less certain outcomes - since the transition to a machine-based civilization might be a disruptive one. When most humans become redundant and unemployable, it isn't immediately obvious what will happen to them. No doubt here will be nature reserves - but a nature reserve that accommodates ten billion humans seems as though it might face significant budget scrutiny.
The article (irritatingly) contrasts biological and cultural evolution - as though culture is somehow non-biological - which is a newbie mistake. Even a full-blown memetic takeover wouldn't be "the End of Biological Reproduction". Cultural reproduction is a form of biological reproduction because culture is part of biology.