I'm having this problem too. Thing is, it used to work fine but I recently got a new computer with an actual graphics card, and it doesn't work any more. Could it be something caused by using an Nvidia card?
I got around it by using numpad 1 and 3 to turn and 0 to fire. It works well, but I do miss those arrow keys.
Works for me on 4.11.3, though I'm binding my keys from within the game (tested both with the Controls menu, and by entering the bind leftarrow +left commands on the console).
Noteably there's no bind there, maybe that makes a difference? Idk... But yeah, right and left arrow do not turn me, at least not audibly. I don't know if they're doing anything visibly since I'm blind.
-Michael.
Edit: those bindings are in the [Doom.AutomapBindings] section.
Edit 2: I got it to work, I needed to move it to the [Doom.Bindings] section.