I am like some others in that I discovered D&D before I read the Hobbit. Since then I truly have been influenced most by what you term chivalric tales and poems. My bookshelf is full of Malory, Steinbeck, Tennyson, etc. Interestingly enough it's equally as full with Historical accounts of the middles ages, the evolution of the English language, some of what you deem Mythical, most interestingly is Beowulf in a few versions as well as classic fantasy and pulp fantasy books.
When it really comes down to it, I should pick other: History. My romance with the medieval period and in fact, all periods of history, excepting modern; and even more accurately, my love for the romantizations of those periods in epics, chivalric tales and even pulp novelizations of the likes of Ann Marston, Michael Moorcock and Glen Cook, is what has most influenced my further love for gaming after I discovered gaming.