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The world is constant of change. Traditional way is more of a physical and can accommodate huge number of players but often have their own interpretation of the games whereas the computer games even at the next room we still can play.
Sometimes it is an advantage to play computer games because for some reason some students chooses their own friends might as well some will be left behind.
A few points I haven't noticed mentioned, though admittedly I may have missed them.
First, if you are an educator you should know about the theories on modalities/learning styles, or the "different intelligences."
Traditional games offer more to the kinesthetic learner, since there is something to actually hold and touch, more so than there is on a computer screen...even if they were playing the same game.
I'd also think about cost. While many schools will have lots of computers, software licenses can get very expensive. 10 packs of playing cards will cost far less than a site license for just about anything, and you can play scores of games with them.
I'd also agree with others who mention the "wait to play" aspect of computer games in the classroom. Most rooms don't have enough computers for a whole class to be going at once, and most schools' computer labs have tight schedules requiring a lot of advance planning to get access for your class.
I taken some of my personal games in to my class occasionally and students like to sit around during lunch and play Blokus or other strategy type games. (Pente was also popular as was Six, Connect 4, Hex, and a few other of the NestorGames) I have also in the past taught some of my students traditional trick taking games like Pinochle.
I think the trick about using games in the classroom is to make sure that you are getting the kids to think while they play, and plan ahead and have some sort of strategy while they play. If they are simply playing to play, and not thinking while they do it, they might be having fun, but they aren't learning from the experience.
And of course you could always teach kids games like Chess or Go, who would argue those require no higher order thinking skills?