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The war is not shown. They slightly implemented it in a scene Jobs ragefully confronts Bill Gates at the telephone, shouting to him about the alleged plagiarism of Apple word processors perpetrated on the Word software from Microsoft and threatening him of legal action, while he meanwhile insults him in a very exaggerated manner, and ending smashing the phone. We never see or hear Gate's voice, as Microsoft is less depicted as a rival than IBM.
Check "Pirates of Silicon Valley (1999)", which focuses on the rivalry between Steve Jobs and Bill Gates. Edit
It is "Breakout", one of Atari's most recognizable masterpieces, which Jobs was indeed asked to re-develop (then it had to be done mainly by designing the main motherboard of the arcade system), but asked Wozniak to do in his place. This allegedly did not bother Wozniak too much, but the fact that Jobs inequitably distributed the salary without telling him (as depicted in the film) was one of the main elements which led to their break-up in the 1980s. Edit