Thats weird. Banner Saga devs claimed to have worked on *technical issues* which prevented a drm free release for backers originally (we thought it was a lazy copout and them removing steamworks) --> in theory Banner Saga on steam *should* still require steam unless they changed things....
Details: I bought it on this winter sale, downloaded and tried 'misplacing' the file about a week ago. It's "The Banner Saga - Deluxe" edition (the only difference from the normal one that was mentioned on the store page was the inclusion of the soundtrack). Mind that it still pops up a message with a warning.
How long ago was that situation with *technical issues*? Do you know if anyone tried to run the Steam version without Steam client back then?
No rush with these questions, I'm not very likely to be online to read the answers before the end of the month anyway.
Update: copied the game to my laptop and it runs without any error messages. As you can see on the screenshot, Steam isn't running.