Brora has always been relatively "upscale." I'd say the demography of its membership is not much different than Dornoch's. It has always been a very popular summer resort for the English, many of whom have summer homes there, already.
I doubt if the new flats will be any more or less obtrusive than is the Links Hotel, which as Neal says, has seen better days. The 6 townhouses built to the north of it in 1996 (referred to in the article) blend in pretty well. I don't think they will have much trouble selling the flats.
As for the sheep and the cows, that is an issue more of local politics than yuppification. I do think that the club (which is controlled by the locals) does want to terminate the right of the crofter to use the land, but I am not sure that this would not be a good thing for the course. Yes, it would take away some of the quirk, but it will improve its playability and maintainability. Should the club maintain an anachronism just to please the whimsies of its occasional visitors? I'm sure some would argue yes, but isn't that being a bit selfish?
As others have said, local economics is a driving factor, and Brora is not a particularly wealthy place. It's main employer (a woolen mill) has closed down, and upscale tourism is probably its best bet to replace some of those jobs. Yes, Brora will change, but it's been changing for all the 25 years I have known it (it had a green keeping staff of one man and his tractor in those days!). Much as we may not wish or want to admit, life does go on, even in the Highlands........