Malcolm, come on, ruled by the king of Scots, yes, Scottish, as in Gaelic, quite possibly not, or only partially so.

I know that you know this but...
Scotland seems to have been, at that time, a mix of ethnically Welsh, Scandinavian, Flemish, French, Gaelic (I could put Irish for that but, suffice to say, the medieval Gael was fully aware of his cultural ties to Ireland), English and the Gaelic/Pictish mixed population(which seems to have been overwhelmingly Gaelicised by this point, I did have a reference to a manuscript that refers to the last Pictish speakers in an area but I think it was before this time. It was also about rights to land between some Scots and some French clergy, the Scots seemed to have been saying "well, this land was inhabited by our forefathers who were Pictish until quite recently, so the land should be ours").

so, um, yeah, Scottish as in from the geographical area of the Kingdom of Scotland. Scottish as in from one of the many different ethnic groups in the kingdom. Scottish as in Gaelic? maybe, possibly not.