Welcome on board, James in London!
True, true, those weird things which occupy space in the wondering Royal watcher's mind...
The Omani sapphire and the ruby necklaces are two different ones. The ruby tassel necklace indeed resembles the famous Duchess of Windsor ruby tassel necklace... and Dyanasty-esque isn't a bad description either!
Diana's ruby necklace was part of a parure with matching earrings and bracelet. Necklace and bracelet were only seen once in public - so it must have been rather too grand for her taste, I guess. Much more elaborate than the Omani set. But she continued to wear the matching earrings, sometimes replacing the dangling ruby tassels at the bottom with drop pearls.
As this modern set appeared at the same time (fall 1987) as the other gifts from the Gulf tour, I'd say it's likely that this is the origin of the rubies as well...
...the others, apart from the Omani sapphires, probably being the large aquamarine and diamond earrings and the cabochon amethyst suite.