The story seems to me in many ways to be anti-Romantic: the solitary man does not find solace or comfort when alone in nature, for example, and there is little interest in the character of the wife. Still, the story does have at least one aspect that is very much in keeping with Romanticism; the story (much like Irving's other stories, including "Rip Van Winkle") is essentially a transplantation of the European (or German) fairy tale onto American soil. Romanticism is the period of nation-building, particulary in younger and only recently unified or independent countries, such as Germany and the United States.
I haven't given you any quotations, I know -- and I apologize for that -- but I hope that these comments may be helpful to you nonetheless.
romantics have bent of mind towards devil. they gave us a new interpretation of satan in literature like william Black , p.b. shelly. they showed us sympathy for satan by calling him a tragic hero... so in this context we can study'The Devil and Tom Walker' that deal with romanticism.