Then you have to read up on the technical spec of your screen.
For this screen, the most likely connection type are: Composite, S-Video, Component.
The Apple cable is a Composite connection.
The screen vendor may sell an adapter cable.
So, if the screen accepts Composite, then all that is needed is an appropriate "dumb" adapter cable to fit a round hole into a square peg. If vendor doesn't sell the cable but gives you a pin-out (tells you what each pin on the cable is) then potentially you can just make your own.
If screen connection is OTHER than Composite then it gets more complicated, you may want to call cousin geeky to take a look, and translate that tech manual for you.