When playing on fullscreen the game actually looks like it is running in a window. I don't mind that but I do mind that part of the game screen is cut at the top.

I uploaded a video which makes it very clear. Mind you I am talking about during a mission so skip ahead few minutes.

https://youtu.be/tS5c1bvx3Ss

That's weird, try pressing ALT+ENTER it works for some games

I already tried it. It does nothing.

Kind of a solution. By pressing F12 the screen gets cropped to be widescreen like which also helps with showing every bit of info. You lose some view but it is fully playable.

Scroll lock is listed as the toggle for widescreen / windowed mode by default, and the 'v' key toggles between resolutions in game. You could play around with these to see if a combination works for you, but if the game says that it's already in fullscreen, I'm not sure how much luck you might have.

Some of the steam users with this problem have reported the problem fixed by using borderless widescreen programs. I believe some fixes for the problem are up at some of the old novalogic fan websites like novahq. I'm not sure how eager I'd be to download and try random internet programs personally, but it seems to have helped others.

Finally, you could look in the main directory and play around with some of the resolution files there. I believe that you can unlock 1024*768. More information here:
https://www.gog.com/forum/delta_force_series/1024x768_for_df1_df2

I'm afraid I can't replicate the problem, so I can't try any of these solutions on my end. I hope something here helps, though.