Working, and working correctly is two different things.

Then the game will be have to be cropped at top and bottom. How is that better?
How do you expect 4x3 ratio to magically convert to 16x10 without stretching, black bars on the sides or cutting top and bottom?

This game was made for monitors that had 3:4 height-to-width ratio. i.e. the monitor was 1.3333 times as wide as it was high. Your monitor is has a 9:16 height-to-width ratio, i.e it is 1.7777 times as wide as it is high. Therefore it is too wide.

It was NOT. Did the Paint screenshot cover the entire screen?

Try this: Take the paint screenshot and increase its size so it covers the entire screen, is it possible doing it without stretching it or leaving two bars at the sides?

OK, since several people explained this already, and you still don't get it, here it is in the simplest way possible:

Imagine you are putting a square peg in a rectangular hole. How do imagine that is going to be possible without either stretching the square, or having the square not cover the entire hole?