In order to answer this question it is important to discuss the pros and cons of games on work computers. I can recall that when I first started to use a computer at work I had a solitaire game on it. We were told to use the game to practice using the mouse and increase our eye hand coordination. I think that it was helpful and fulfilled that purpose. However, for some it became a pastime and they spent a great deal of work time playing these games not for their skills development but for the enjoyment of the game.
Young adults that enter the workforce are very capable in using all the elements of the computer so one could argue that these games serve no purpose. But consider the argument that you can improve your problem solving and reasoning skills by playing these computer games. These are certainly skills that would be valuable in the work place and would make the case for games on your work computer. I believe the argument about whether or not we should have games on our work computers cannot be resolved unless we discuss the issue of the use or abuse of the games.
Spending too much time playing computer games at work is not appropriate; just the same as it is not appropriate to take three hour lunches when you are given one hour. Some employees may take the opportunity to relax or have a bit of a distraction during their breaks to play these games and that could be a good thing but moderation needs to be the main consideration.