Yes it is a region. It is also a country but that doesn’t alter the point. This vote was not like a general election in which regions voted for MPs. Everybody had one vote. Scotland didn’t vote for anyrhing, the people in Scotland voted.
In a view of the referendum as discrete from history and politics, that's correct. Thing is, it isn't separate from those things. The vote in the separate sense gives no more justification for independence for Scotland, than it would if the upper floor in 23 Railway Cuttings, East Cheam voted remain. In the rather more complex world of things beyond the referendum it's a bit different.
Let's have a look at three areas mentioned that voted Remain. London voted remain, and at the time of the referendum there were some murmurs about the possibility of a city state. Indeed there had been some before that but very occasional. There had been a move to devolving powers after the petty power grab by the Tory govt under Thatcher, and an ongoing campaign to reduce local powers in a number of govts. There is no reason why London could not work as an independent city state in Europe, though there might be some practical difficulties (which I'll mention when I get to Northern Ireland). And yet there isn't any real movement to get this as the solution. I have to admit I think that the various parties that might be interested in speaking for London's interests in the last couple of years as regards the financial industry have been quiet, and I suspect that's because it's viewed as suspicious outside of that bubble. In the end though there is no real push for independence and that makes the feasibility of it, low.
Moving onto Scotland - coming a couple of years after a referendum in which the Unionist side argued that the only way for Scotland to remain in the EU was to vote No, and where 45% voted to eave we have a very different situation than London. Add to that that Scotland is a country with its own legal system, education system, and we have in the grand scheme of things a different situation. That said the vote in the EU referendum alone isn't significant to that, it's the significance it gains within that context. It would be too easy though, as some do, to say portray the Yes vote in the indyref, as somehow homogeneous in it's support for the EU. Indeed it's clear that some of the reluctance to hold an indyref2 arises from the worry that a significant part of the Yes vote is anti EU as well and would maybe switch sides.
And then onto Northern Ireland, where the vote to Remain is then fed back into a situation where the practicalities of day to day become significant in a way that isn't true of elsewhere with the land border. I do wonder if the unrealistic approach take to this over the last two years has dampened down any idea of solutions to London's ambitions, and made any idea of a city state as mentioned above seem completely infeasible. Again while NI is no more than 23 Railway Cuttings in the view of the referendum, the referendum is very much more in terms of the feed back loop into the history and politics of NI. The likelihood of a united Ireland has grown because of the vote and what has happened since.