Some psychology behind achievements

There are two different ways people respond to challenges, depending on what do they want to do with their skills

  • Demonstrate their skills, they are interested in proving their performance
  • Improve their skills, they are interested in gaining mastery
This is supposedly learned at childhood, that means culture may have a strong influence in it, and thus Japanese culture may promote RPG games and in the United States FPS may be a more important trend, of course there are other factors that may have a stronger influence in these trends.
Undoubtedly there is a correlation between this personality trait and the style of games that a person may enjoy. Some games reward players for doing something that is just a matter of time, other games reward the player for acquiring a skill.
These skills may be useful in a different context, to start with, most probably the skills acquired playing an FPS are useful for other FPS games, unless there is a sort of overfitting, most probably the skills acquired to use covers (even to walk faster) in Gears of War cannot be used in Halo 3, but at least they are more generalizable than the skills a Fable II character may have, as most probably they won't be portable to Fable III. At the core of games there are some skills and dexterity that cannot be appreciated straightforward but for which chess is often praised and probably more modern (video) games would be too, if they were studied in more detail.
The sense of achievement in modern games varies between people and the reasons that cause this feeling probably depend on the type of game played, but they have to be linked with the capability of the person to abstract the details of the game and in some sense feel as relevant whatever is happening in it, finding some real relevance in something that is only fantasy
The eager for achievements has not been as deeply studied as other related topics, as competitiveness, which require further study too. But even if there are common patterns among people there are probably also important differences as happens with nearly every characteristic in human beings. This means some people have stronger tendency or likes for the achievement porn that may be video games and other activities.
This doesn't mean games should not be played, but they have to be put into context. With the exception of people whose work is related with them, games are just something to spend some time, relax, enjoy and be rested to do something else, something that is actually relevant for your life in a more efficient and effective way, as a consequence of resting before. The same way sleeping is important, leisure time is also important, and in that time people should not be forced to play games, practice sports, socialize or do any specific activity, spare time is spare, the mechanisms that forge personality and cause people to give more or less value to each activity are unknown to a great extent, and, at least as far as they are unknown, a change should not be forced for  the consequences may be very bad.
Games provide a easy way to achieve for those who have a great eager for achievement, and they have a personality fantasy prone enough so that the achievements got from games, very easily when compared with real life, are still rewarding despite of being virtual. But that is good only as far as that helps to achieve in real life. As it usually happens with hobbies, in the beginning they help to rest, they help to get new skills that may be generalized to other aspects of life and they have a positive effect on the person in general. If the person focuses too much on games and the consequences are negative for him or her then it may be an addiction and that would be a problem to solve, which means an additional opportunity to achieve something :)
gl, hf

PS: BTW. If you have a strong eager for achievement as I do, here is a trick to stay on (the real) track, make a ToDo list. Checking a list item may not be as rewarding as watching some cut-scene after completing a campaign in a great game, but it helps to stay accountable. Please let me know if you try and it is useful to you.