1. Most websites will get little to no traffic.
2. Consolidation will eventually result in a mere handful of verticals remaining, in the author's opinion, solely Google and Facebook.
3. At first, content framing tactics, like FB Instant Articles and Google AMP, will result in these providers obviating the need for users to navigate outbound links; instead, the content will be surfaced from within the ecosystem.
4. Content providers (i.e. "publishers") go along with the above because in truth they are desperate for revenue. Giving away content for free in exchange for the potential of display ad revenue due to high volume is seen as their only realistic hope for survival, making this a coercive relationship.
5. Some strange political speculation, but, notably, the two giants banning people and services who have presence on the other. Also, independent newspapers get bought out and absorbed.
Out of this distillation of claims, #5 is complete baloney more egregious than an industrially-processed slice of knockoff Mortadella; beyond even a fanciful fantasy of how these companies work. Claims #1 through #4, on the other hand, are very astute predictions, or rather, observations, as they're already here.
The long tail of websites is pretty long, and most sites indeed get very little traffic even today. One need not look further than the power of communities like HN and Reddit to slashdot all sorts of sites by overwhelming it with legitimate traffic. This brittleness and inability of some sites to scale to momentary demand, along with ISPs forbidding home servers and the risk of malicious denial-of-service means that the original way of self-hosting sites on the Web is largely dead [1], or at the very least, a risky call. This unfortunate fact means you probably want to pay someone to host your site instead. Though there are thousands upon thousands of professional hosting providers, it's a dramatically smaller number than the number of websites; so we're slowly walking up the tree of vertical consolidation.
#3 is well-documented, and #4 follows naturally from the tribulations of finding business models that work on the web [2].
I stand by the view that #5 is too much of a leap; willingly excluding potential customers seems like an act of folly -- Home Depot doesn't ban anyone who shops at Lowe's, but instead they'd love to lure them away. Orthodox airlines in the US at time of writing might as well be regarded as quadrupoly: they have suspiciously similar ticket prices for most non-hub destinations, and they have semi-secret programs to offer matching frequent flier status to the topmost tier of most profitable travellers if one wants to jump ship.
Nonetheless, there is in fact a real emergent phenomenon in the continued vertical consolidation of content silos. Apple -- mysteriously absent from the author's narrative -- is the exact sort of player whose excellent products, dedicated fanbase, and seeming benevolance will result in the sort of transformations that the author fears: Apple has doubled down on producing original content [3] for its captive ecosystem, following the tactics of Amazon and Netflix, but unlike them, Apple's presence does not extend horizontally to other platforms. In fact, we just had a trending article [4] which covered in-depth the different tactics companies use to achieve reach and retain customers.
It's more believable to envision a future similar to what happened to major US television networks: NBC, ABC, CBS, Fox, and Turner; lots of mergers and intrigue, phases of ownership by movie studios, phases of ownership by seemingly unrelated enterprises that pivoted to holding companies from something else, acquisitions in efforts to form new verticals; and yet despite all this, there's still several of them. They're all deeply vertical now, but their valuations and regulatory pressure keeps them existing side-by-side.
[1] https://news.ycombinator.com/item?id=14699084 [2] https://news.ycombinator.com/item?id=12299230 [3] https://techcrunch.com/2017/08/16/apple-said-to-be-spending-... [4] https://news.ycombinator.com/item?id=15082966