Add a game capture for Diablo II. Go into the properties and select the "Use Hotkey button".
Then open the game, start your stream - you will get a black screen. Now press F12 (default hotkey) and picture starts. Only sad part is - if you minimise the game or switch focus from the game window it will go back to a black screen and you will have to restart the stream.
Seems like some issue with 1.10 (notice how when you click away from the window it gets blacked out & minimised automatically), might just be easier to use desktop capture.