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The Omen - Artist Edition would be considered deluxe, in that it includes a new forward by David Seltzer, and multiple full colour internal illustrations by Juliana Kolesova with printed offset on archival Cougar Vellum paper and the Endsheets are embossed rainbow paper. So it's both limited, and deluxe in that sense. Because all a deluxe edition means is extra content of some kind, compared to another edition. In this case, we'd be comparing a limited Suntup Press edition to standard paperback and hardcover editions previously released.
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It's also tricky to call all editions deluxe because Suntup Press, Dark Regions Press, Centipede Press, Subterranean Press etc are all limited compared to Folio Society and Dragonsteel and Discworld Emporium, so you're more likely to get a higher quality of production as well as extra content extending beyond illustrations like how Suntup's Charlie and the Chocolate Factory included deleted scenes and handwritten letters by Raold Dahl. But on the otherhand, because Folio Society does a lot more "standard" Premium editions, you get a lot of really gorgeous editions to books without the anxiety of it being limited, and there's more of a variety because they can come out with like 10 new releases for a season, which is something a limited production can't do. And other sites that do standard releases , occasionally release their own deluxe limited editions or special editions of some kind. You then have non-deluxe limited edition releases like from Illumicrate, where they just offer a gorgeous new look to the book and sprayed pages, but no actual new content.