Almost all political positions are Nationalist at heart, it's kind of the point really, it's just that the UK Government defines the 'Nation' somewhat differently to Holyrood, and this is totally to be expected considering Holyrood is designed to represent just Scotland and therefore considers National issues as those involving Scotland, whereas Westminster consider National issues to be those involving the the Union.
The situation is a bit of a mess really, I remember the Poll Tax being issued in Scotland a year before anyone else got it, as an 'experiment', that sort of thing sticks in the public psyche and gives a very definite impression of your position in the pecking order from the perspective of Westminster.
Is the SNP 'Nationalist' in the way it is meant here, that's a difficult to answer, they are Separatist for Nationalistic reasons, certainly, but it's a chicken and egg question, is thinking Scotland would be better off without the rest of the UK 'Nationalist' or does it depend on whether that is true or not?
That said, the Scottish people have spoken twice, they've voted in the SNP as the power-incumbent for Scotland and they've voted to remain a part of the Union, which is a defiance of the core tenet of the very party they later voted in. There's a feeling of remoteness from Southern England, both physically and politically in Scotland that Westminster simply fails to connect with, the SNP provides that 'homegrown' feeling but I don't think Scotland want independence, they just want to feel someone 200 miles away gives a ****.