Where to start...
As badly written articles go, this one is... quite badly written. Where to start?
First, the entire article is based on the strawman that a basic income policy is only intended to address a shrinking job market. However, there's far more to it than that: not only does it reduce inequality and poverty (pleasing the left) and reduce government bureaucracy overheads (pleasing the right), but it also leads to more entrepenureal activity (pleasing both). After all, if you have a guaranteed economic safety net, you're free to experiment and take risks that would be unthinkable otherwise. And this isn't just a theory: this effect has been seen in many of the pilot schemes carried out to date (https://en.wikipedia.org/wiki/Basic_income_pilots) - in Madhya Pradesh, "The study also found an increase in economic activity as well as an increase in savings, an improvement in housing and sanitation, improved nutrition, less food poverty, improved health and schooling, greater inclusion of the disabled in society and a lack of frivolous spending".
Dismissing the concept as being just "charity" is therefore both foolish and misleading - as is the claim that it would "not be progressive or emancipatory".
Then, there's the shoe-factory example. There's an underlying assumption here that there's an infinite market for shoes - i.e. if you make 200 pairs instead of 100, you can sell all 200 for the same price as the original 100. In practice, the market will become saturated sooner or later, and then you'll have to either drop your prices or reduce your output. Either way, that shop-floor worker will lose out, as they'll either get fired, work less hours or get a reduced wage.
"There's no correlation between how burdensome and how well-compensated a job is". "Burdensome" generally isn't factored into compensation calculations because it's irrelevant (and often subjective, to boot). A manual job may require some degree of physical fitness but often requires little in the way of training or experience, so there's a very large number of people who can do it and the laws of supply and demand kick in again.
"The principle of production increase over leisure increase applies independently of the type of job in question". It does up to a point - the point where supply exceeds demand. At that point, you either scale back, start making a loss or end up with a large chunk of unsold/unsellable inventory - which essentially also means taking a loss.
Then, there's the claim that there will be new jobs to replace the old jobs. However, the current industrial revolution is different to previous ones in at least one important way: it's happening a lot quicker, and it's affecting many more economic areas. After all, a lot of it is being driven by software, and new apps and updates can appear virtually instantaneously across the world. Take Google Maps for an example: it's eliminated the need to keep a physical map in the car, and it's getting increasingly better at identifying and routing around traffic jams. So there goes the paper-map industry *and* the traffic-report DJs. Along with everything else that can now be handled by a mobile phone - checking your bank balance, taking photos, booking hotels, ordering food, checking mail, etc. There goes the bank-teller, the camera-manufacturer, the people on the phone and even the computer manufacturers...
Admittedly, people are using technology to create new jobs for themselves - t-shirts, 3D printed cosplay accessories, self-published media, etc. Sadly, the people I know who do this are generally making little or no money. Because with technology being so cheap and easy to use, anyone can do what they're doing and the rules of supply and demand have come into effect once more. However, having a basic income would give them more freedom to experiment, innovate and differentiate themselves, and therefore increase the revenue they earn.
It's actually worth looking at some of the classical civilisations to see how they handled over-production and over-population - Egypt, India, China, etc. Generally, what you ended up with was a heavily striated society with very limited movement between layers and increasingly complex social models and policies - such as the imperial examinations in China, where you had to study philosophy, poetry and even horseriding and archery. They also tended to have either low productivity or some form of resource-sink, such as the Great Wall of China or the Egyptian funeral industry. And in the long run, they also tended to be dominated by more efficient and less striated civiliations - the Romans, the Mongols, the British empire, etc.
Of course, there's always another approach to dealing with over-population: going to war - not only does it reduce your population (and that of whoever you target), but it distracts the general population and you also get to spend resources on equipping and training your troops. Win-win, except for the people at the sharp end of the axe.
So personally, if a Basic Income offers even the slightest possibility of avoiding a striated society or war, I think it's something we should be spending a lot more time looking into!