How could I make the game fill all the screen without these black stripes on the sides?
I do not think that is possible. M.A.X. was released way back in 1996 when most all monitors had 4.3 ratio or 4 wide to 3 high. A popular resolution back then was 800 x 600 which was massive in its day. Again 4.3 ratio.
While some games back then had different resolution setting so if your system was powerful enough you could get better quality graphics at a higher resolution. But for the most part the ratio still stayed the same.
Most all of today's monitors are considered widescreen so they are much wider than they are tall. Unfortunately M.A.X. does not have a widescreen setting. It is stuck at 4.3 which accounts for the black bars you see on the sides of the screen.
I am playing on my 24 inch which has a native res of 1920 x 1200 which is 16 by 10. I use the monitors zoom function which increases the play area to the top and bottom of my monitor but I still have the bars on both sides of the screen.
Still corner to corner is close to 22 inches which is massive when I think I once played it on 14 & then 17 inch monitor back in 1996.