Like a lot of things in this blog, my understanding of "pulp fantasy" is idiosyncratic. I don't use it as a term of opprobrium, since I adore the genre and read it voraciously, including the works of lesser authors whose ideas and execution are often deeply flawed. While pulp fantasy has a lot of different elements that draw me to it, the one that stands out is its powerful focus on individual wants and desires, thoughts and feelings. The goals of the protagonist -- and often his antagonists -- are what's important and everything else are largely obstacles to or consequences of that individual's peripatetic search for his (typically ephemeral) intensely personal destiny. That's why I view Moorcock's Elric tales, for example, as pulp fantasy, even though they're set against a backdrop of a cosmic battle between Law and Chaos. In the end, that battle is secondary to the battle within the character of Elric to find his place in the world, as it is in most pulp fantasy.
For that reason, I feel comparatively little shame in dubbing Gene Wolf's 1980 novel The Shadow of the Torturer a pulp fantasy. This book and its three sequels tell the story of Severian, an apprentice Seeker of Truth and Penitence, which is to say, a torturer. Unfortunately, Severian chooses to be merciful to one of his charges, allowing her to commit suicide rather than suffer, thereby breaking the oath to his fellow Seekers. Rather than being punished with death for his oath-breaking as he expected, Severian is instead sent away to a far-off city to serve as its executioner, precipitating the beginning of the protagonist's many travels and his growth and development into one of the most interest characters in recent literature.
The Shadow of the Torturer is an extremely difficult book to characterize. It definitely occupies a similar place as Jack Vance's Dying Earth novels, taking place in a world so far in the future as to be beyond time. Like Vance, Wolfe effectively uses language to convey the decadent antiquity of his setting, Urth. Through a combination of English archaisms, Latinate neologisms, and words purely of his own invention, the text can sometimes prove hard going. Additionally, Wolfe maintains the fiction that the novel is in fact a mere translation from "a language that has not yet achieved existence," which, when combined with the unreliability of Severian's first person account of his activities, creates further levels of complexity and nuance.
I read this book long ago and dismissed it out of hand, mostly because I found it impenetrable. Fortunately for me, I read some articles about Wolfe that convinced me I'd missed out on a classic of science fiction and fantasy. I then took my time and re-read The Shadow of the Torturer and very soon thereafter made my way through the rest of the The Book of the New Sun series, very much enjoying it. There's a great deal going on in these books, on both a dramatic and literary level, and it's an amazing thing to behold. Wolfe's talents as a writer are unique; I can think of no other fantasy/science fiction author else who manages to achieve what he does in this series of books.
Because of publication date, there's no question that The Shadow of the Torturer exercised no influence over the development of D&D or AD&D. Even if it had been published earlier, I'm not sure what kind of influence it could have had. Though there are certainly lots of things within it, such as Severian's sword Terminus Est, that I can easily see some gamers swiping for use in their campaigns, doing so strikes me as far more crass than any of OD&D's borrowings from Tolkien, the author whose work strikes me as closest to that of Wolfe and even his closeness is limited at best. Nevertheless, I highly recommend Wolfe's work. It is not an easy read by any means, but it does repay the time and energy spent in working through it, making him one of the few authors I've ever given a second chance.