Not according to the Chinese government. Whereas the UK government does say Scotland is a country. For someone who values the UK constitution so highly you play pretty fast and loose with it when it suits.
I've already pointed out: the UK government is perfectly allowed to use any terms it likes to refer to the regions of the UK. And the UK government knows perfectly well that a certain proportion of residents of England, Wales, NI and Scotland like to think that their region is a country. So it's politically expedient for the UK government to use that nomenclature.
Maybe yet another analogy will help illustrate the truth here. In politics, and specifically in respect of UK (and regional) governmental organisation, the word "secretary" has a particular meaning and status. If someone is a secretary in government, this has a very particular and very high-status meaning. Which is a very different meaning to a secretary at a law firm, for example. Likewise, in international politics (especially European politics), the term "chancellor" describes the head of government. In the UK, for reasons of historical anomaly, the term "chancellor" describes the head of the finance ministry of government. So the UK chancellor is, indeed, the "chancellor" within the narrow UK definition, but under any wider definition (s)he is most definitely NOT the "chancellor", but is instead the "finance minister".
And thus it is in international law and colloquial usage with the word "country". Scotland (and England for that matter) is not a country under the commonly-understood international political/legal sense of the term. But that is not to prevent anyone from referring to England or Scotland as "countries" (or even "nations" for that matter), provided that everyone is aware that this is merely a colloquial local usage of the term and not a usage of the term under the commonly-understood international political/legal sense of it. Just as with "secretary" and "chancellor".
ETA: For yet another comparator, plenty of people (and some official bodies) refer to Wales as "the Principality of Wales". That is their prerogative. But it DOESN'T mean that Wales is actually a principality in the accepted definition of the term. And Wales is, of course, not a principality in the accepted definition of the term. The fact that it ONCE was is neither here nor there in 2016. Scotland was once a country. England was once a country. In 2016, neither are countries, regardless of whether or not they like to refer to themselves as countries.