As I recall it there are two main aspects to this, one of which isn't mentioned in the article.
Uber doesn't charge VAT on the fees it charges drivers because it charges them via a Dutch subsidiary, thus no VAT chargeable under EU law. That's where it differs from a standard UK despatch operation, and indeed other app-based platforms in the UK.
The other dimension relates to the relationship between the platform and the drivers, as outlined in the article, and while I'm not sure if the VAT arguments are precisely the same as whether the drivers are employees or self-employed, there does seem to be a big overlap.
And, of course, to that degree the argument applies equally to other app-based platforms and more traditional UK operations
So there are two elephants in the room as regards that article - first, that Uber is different in that it charges drivers via a Dutch subsidiary.
The second is that the employee/self-employed issue is also applicable to other UK operations, and to that degree the VAT issue is the same.