Well, in the first instance, "links" courses are really classified as such by the type of soil and turf they are played on - links courses are on sandy soil which drains well and can generally be left to their own devices, not requiring much manual watering above and beyond what nature provides. So I don't think "links style" means what you think it means.
That said, to answer the question I think you're asking: it varies at Dunbar from hole to hole. The 6th and 17th holes run parallel to each other, and the ideal line off either tee often involves hitting into the opposite fairway. On the 1st hole, you can bail out to left off the tee into the 18th fairway or sometimes even to the right into the 2nd fairway, and there are other holes like the 2nd and 18th where you can bail out into a parallel fairway. But there are plenty of holes - the 4th, 8th, 9th, 11th, 12th, 14th and 15th, not counting the par 3s - where both sides of the fairway are guarded by rough, water and/or OB and there isn't an obvious bailout line as such. (The 4th in particular is a short par 4 with a landing area that can feel frighteningly narrow: beach to the left, OB wall to the right.) So it's a nice mix.
And yes, the course is beautiful - I try to keep reminding myself of that, particularly when my scorecard is going to hell. It's beautiful in a rather refined way; I'm more of a fan of other links courses with wild dunes and humps and hollows and elevation changes, but Dunbar for the most part is relatively flat, and there are no dunes adjacent to the course at all. But it is right on the water in the way that few other links courses are, and the views back to town, out to sea and of some of the amazing rock formations between the course and the sea can be rather splendid. (And to reiterate: my standing invitation to host other SoSHers out here remains open, so once the pandemic subsides enough to allow overseas golfing tourism, I'll hope to see more of you out here in due course!)