Playing games have two primary benefits: mental elasticity and fun. If you throw in a language requirement, meaningful context, and social interaction the benefits increase exponentially.
Let me present an example:
There's this nice little thing called "Happy Cube". (I presume it has other variants as well.)
The Happy Cube is a three-dimensional puzzle. The puzzle pieces are made from nicely colored and pleasant-to-touch styrofoam. One Happy Cube set has 6 puzzle pieces which are used not to form a flat square, but a regular cube in three dimensions.
There are many sets, progressing from easy to solve to harder (the pieces become less symmetrical and repetitive.)
successfully assemble the cube, you have to touch and feel, explore many possible variations and connections, look at the constructions from many perspectives, and try many approaches to attempting to solve the puzzle.
This process enhances mental elasticity; creates an open attitude and new ideas which can be successfully used in more complex situations.
Playing this simple game is fun. Fun/joy is a very important aspect of learning processes; some would say it is meaningless, but it is the very thing that gives unquestionable meaning.
If the fun and joy are gone, the connection between the learner and learned is gone; no matter how 'important' a subject is deemed by external standards.
Look for fun in learning, for only that keeps it going forward.
The schooling system has degraded the concept of 'learning', so for true and efficient learning look for situations where it's "just play".
(Even 'mindless' shoot-'em-up computer games are efficient exactly because they are 'mindless': the mind acquires faster ways of thought rather than just standard linear thinking.)
As the complexity of games arises and with it the ability to absorb and comprehend systems and complexes, so does this ability become increasingly applicable in the complexity of the 'real world'.
Not all games are win-or-lose, fail-or-pass; games with open worlds provide unbound creativity. (For example, the simple world of the Happy Cube, where the puzzle pieces of all sets are available, and not just cubes but many other shapes and forms of various sizes can be created.)
From simple games of chance and imagination to the virtual worlds of modern massively multiplayer games, playing presents much learning potential.
In fact, the only way to learn anything is to play with it.