The claims about its increased frequency are discussed for American English in this post by Neal Whitman from February this year, and are true. It is getting more common (this is super-unusual, by the way, because normally it's the frequency illusion). Whether the claim that its use over here comes from American English is true or not I don't know; I can't be bothered to check because I don't really care.
What I do care about is whether it really is a prefix in all the examples they mention. Neal has it as an adverb and I instinctively classed it as that as well before I was pointed to his post. Why, though? The Oxford Times' examples are all written with a hyphen, and they explicitly call it a prefix. I also have an intuitive hyphen when it's an attributive adjective rather than predicative (a super-compelling argument vs this argument is super compelling). Whyyyyy??
[Aside: the fact that it can be unambiguously an adjective in examples like This pudding is simply super is irrelevant. Words don't usually have a category* when considered in isolation, and only have categories when considered in context.]
With a noun, as in superyacht, I'd not hesitate to call it a prefix, regardless of whether it's written like that or as super yacht or super-yacht. And when rich is a noun, I'd class it as a prefix (the super-rich ought to pay more taxes), but when it's an adjective it's a more ambiguous (The owner of this company is super rich). This is easily explained: adverbs can't modify nouns, so super (adverb) can't modify a noun like yacht; it must be a prefix meaning something like mega- or über-.
So let's focus on the ambiguous cases where it modifies an adjective, so could be a prefix (like über-strong) or an adverb (like incredibly strong). How do we tell which it is? Intuition is notoriously unreliable.
It would be useful to know if anything else can occur between the putative adverb and the adjective. You couldn't split a prefix from its base (apart from with expletives, like un-bloody-fortunately) but you might be able to put another word between an adverb and an adjective (really very pleasant). I don't think you can with super, but it's not a super-compelling argument; you also can't put anything between very, an undisputed adverb, and an adjective (very really pleasant is awful). But you can stack it up, which is more adverbial-like (super super happy).
One argument for it being a prefix would be that it can modify just adjectives. Adverbs can modify verbs and prepositional phrases (not nouns, as noted above). But it looks like super can actually modify these too: Neal Whitman gives these examples of prepositional phrases:
Three is super off tee, but not off turf.Other adverbs:
I was super into rollerblading which I'm not any more.
Lift super slowly, taking 10 seconds to raise and 5 to lower.And verbs:
My job was to 'appear', super suddenly.
Their media strategy... is to kind of exalt and super serve the conservative media.The fact that these are less common is slightly an issue, though - perhaps this is a prefix in the process of breaking free and making a bid for adverbialhood? It's times like these I wish I was more of a morphologist and knew how to find out. Advice welcome - anyone want to do a study?
I super hate to lose.
I super want a desert tortoise!
We super like this song.
*That's a super-controversial way of putting that. I don't mean to imply any stance on whether the category of a word is part of its inherent content, or whether the same word in more than one category is a single word that changes category rather than being two homophonous words, or anything really. I have opinions about these things but they aren't the point of this post.