Technically, yes, but when they're talking about this sort of thing, they mean "personal recommendation system" or "content-based recommendation system."
For example, the HN front page is a recommendation system if you literally mean system-that-recommends-web-pages-to-look-at. But it's not personalized; every visitor sees the same front page. This fundamentally makes it a different sort of thing.
If You have 10000 posts that You have to sort it in some way and the user just going to see 20 of those, the sorting is the recommendation system, people are just used to think of products, movies and songs, but in those platforms the users are the products
This hardly seems like a reasonable way to characterize Netflix, which has a personal recommendation system, especially compared to HN, which is ad supported yet gives the same recommendations to everyone.
My reading of their comments is that they are trying to say that social media and news media can be characterised as having recommendation systems too, not just song and movie platforms (I don't know who exactly they're arguing against – I've never heard anyone say that recommendation systems can only be for songs and movies).
I don't think they're really paying much attention to the dimension you're splitting it along, i.e. whether the recommendations are personalised for each user. The huge important idea they have in their head is that recommendations can apply to user-generated social media content too.
Yes, but this is an extremely important dimension to split on. The practical implications are so big that the game changes completely.
* HN and classic Reddit sort their items on a single dimension ("hotness"), calculated using a few input variables and producing a single output variable. This is about as cheap to calculate as recommendation systems get. The XKCD comment recommender is a bit more complex, but still in the same complexity class. Since the whole point of an algorithm like this is to be timely, the naive approach is to compute it on-the-fly, which it's perfectly simple enough to manage.
* At a somewhat more complex level, you get stuff like a basic, uncustomized Similar Items list. If YouTube has no data on you, this is what you get from their sidebar recommender (and their front page would be analogous to Reddit and HN, but sharded by region and language). It's also pretty close to what AdWords used to be, before they started doing user profiling. The thing with this method is, even though it involves some level of AI, it's presenting the same thing to everyone and it's expensive, so the natural solution is to precompute it.
* Personalized recommenders are the worst of both worlds. You can't naively compute it on-the-fly, because it's too slow, but you also can't naively precompute it, because there's a combinatorial explosion of users and items. You actually have to be clever about it.
