His help in creating Spacewar! was invaluable, although not necessarily conventional. In one memorable incident, Alan forced Steve Russel (the main author of Spacewar!) to get his act together by calling up the maker of the PDP-1 to get some math routines required to write movement code for the game. Once he'd received the code he slammed down the tape on Steve's desk (who was widely known by the nickname "slug") and said "Here you are Russel. Now what's your excuse?" Steve got the point and went on to finish Spacewar!
Had Alan not taken the initiative like he did, the entire history of video games could have turned out differently. A man called Nolan Bushnell was later inspired by Spacewar! to try and make video games accessible to everyone: he eventually went on to found a little company called Atari. There's nothing to say that games wouldn't be as popular as they are today had Alan not given Steve Russel the kick up the arse he needed, but it certainly makes you think.
Another of Kotok's achievements was working with John McCarthy of Stanford to create the first computer program that could credibly play chess. The program, which could look at 1100 positions per second, took part in an international competition with a USSR chess program in 1966. The match took nine months to complete!
Alan is survived by his three children and one grandchild. His wife, Judie, passed away last year. Rest in peace, Alan.
Update: see comments.