Work and Play had a baby named Game. Its purpose was to make us find solutions to its problems - and like it. Checkers, chess, and even classic card games all use symbols and rules to push their players to think. No one would argue against the value of learning strategy in pursuit of success. Right?
Modern video games incorporate the most engaging forms of media and storytelling to usher folks past the screen and inject them directly into the puzzles. Nowadays, these obstacles range from taking route 'A' and eliminating enemy 'B' to identifying patterns in colors and shapes to understanding the physics of hurtling birds and compensating their trajectories or, even better, how navigating inter-spatial wormholes affects a course's momentum and direction.
If that last one sounded made up to you then you clearly have not been fortunate enough to experience Valve's Portal. The only real violence in the game is the brainstomp it delivers as you try to wrap your head around the mechanics for the first time. Seriously, play it. You'll learn more than you think.
The point is that video games are simply a more evolved and involved form of manufactured problem solving. Hell, how many people still bothered to play (and shuffle) solitaire with paper cards once it translated to the screen? All the rules and techniques were there but in a cleaner and easier-to-use format. More thinking and less handling a sticky deck of cards.
Some titles also extend its tools to users to allow creation of their own environments and puzzles for their peers to complete. Enjoyment of one, translated into work for the enjoyment of others. Splendid. Despite the industry being villified on more than one occasion, I think many would argue in favor of the benefits the medium has (and will have) to offer. Play is on the cusp of accomplishing great things. It's just a matter of finding the right problems to solve. Like science! And then more science!