I don't know Gary Gygax's preferences in regard to authors of fantasy fiction, but I feel pretty strongly that L. Sprague de Camp (1907-2000) is the closet in sensibility to Gygax himself, at least in the earlier days of D&D.
De Camp makes several appearances in Appendix N. I haven't read all of these works, but the ones I have read demonstrate some characteristics I get from Gygax's worldbuilding and from his early fiction that I have seen. There is some content similarity (like universe-hopping, crossovers with the works of other authors, and hierarchical planes of existence), sure, but what I'm mainly thinking of is more of a structural or attitudinal alignment.
For one thing, I think it's fair to say that Gygax's work shows a concern with realism and degree of pedantry around certainly topics: Extensive list of polearms, obscure terminology, etc. De Camp gives us an extensive exegesis of REH's naming in the Conan stories and also an analysis of the same stories' technology. He wrote a series of Sword & Planet stories (the Krishna series) that makes a point of addressing the unrealistic elements of Burroughs' and others' similar stories.
It seems to me there was a logic to Gygax's D&D work. I'm sure this is in part due to it being in a game where you have to be prepared for player action, but it resembles the application of rational consideration of elements in fiction as in the Harold Shea stories or The Carnelian Cube.
Both men also have a fondness for humor in their fantasy. While this isn't an uncommon trait and is found in the work of a number of Appendix N or adjacent authors, I feel like use of anachronism for humorous purpose is something found in Gygax's work that also occurs in the Harold Shea series. Less than totally heroic or unheroic protagonists (often the humorous effect) probably describes a lot of D&D, but also several of de Camp's Krishna novels and his Reluctant King trilogy.
As to Gygax's later work, I've only read a couple of the Gord novels and that was decades ago, but I don't recall them being particularly de Campian. Maybe his sensibilities shifted over time or perhaps they reflect a desire to better compete in the fantasy market that existed in the mid-80s. Still, I think on balance, the similarities are there.