Nice timing, I just got on. XD
I see, that's awfully strange. Hmm, have you tried running the game in windowed mode and using display capture to set it? I believe the way the fullscreen works is it'll put the game window in the top left and set the display to match that resolution. OBS will pick up the rest of the screen while all you're seeing is the resolution you set.
Maybe if you tweak your monitor's resolution in the control panel AND the in-game resolution, and run in windowed / borderless / modal style, that should simulate fullscreen without actually being fullscreen. I'll give you an example:
In the above screenshot, I had the game set to windowed mode, but it appeared to be fullscreen because it took up the entire resolution of my display - I have an ultrawide for video editing. Say you were to go to the display settings in control panel (https://i.imgur.com/8dVkHaK.png) and bump your monitor's resolution down to where you want the game to run. Would that appear to be fullscreen in the stream output, you suppose?
Might be worth testing.