If for whatever reason you don’t want to install the cncnet client you can try some other options. Firstly the graphics system patch DDWrapper is known to solve the “black screen” issue for many people.
Download the zip file and extract “ddraw.dll” and “aqrit.cfg” into your game folder. Then, open the configuration file “aqrit.cfg” in Notepad, change the “ForceDirectDrawEmulation” option to 1, save the file, and the game should work.