i don't know if entertainment and training are mutually exclusive. but i also can't say for sure if there's a causal connection in either direction. one theory of humor proposed by philosopher scientist Daniel Dennett and some of his colleagues suggests that laughter is to learning (having a new thought process - "oh, i didn't know you meant the word in that context. ha" - as orgasm is to procreation. there's likely some evolutionary motivation behind it. i imagine a similar thing might be going on with games. perhaps games are so effective at training us that we're entertained, and so we're drawn to it. some issues here: well it's not necessarily true that everything we enjoy is evolutionarily preferable. there can be false positives. i think of the moths whose moonlight pathfinding mechanism misfires so often (and so recently) in response to man's use of fire.

David Williamson Shaffer is an educational psychologist (among other things) and has some interesting things to say about the perspective games offer. i point to his theory of epistemic frames. from the abstract to his paper Video games and the future of learning:

"Will video games change the way we learn? We argue here for a particular view of games—and of learning—as activities that are most powerful when they are personally meaningful, experiential, social, and epistemological all at the same time. From this perspective, we describe an approach to the design of learning environments that builds on the educational properties of games, but deeply grounds them within a theory of learning appropriate for an age marked by the power of new technologies. We argue that to understand the future of learning, we have to look beyond schools to the emerging arena of video games. We suggest that video games matter because they present players with simulated worlds: worlds which, if well constructed, are not just about facts or isolated skills, but embody particular social practices. Video games thus make it possible for players to participate in valued communities of practice and as a result develop the ways of thinking that organize those practices. Most educational games to date have been produced in the absence of any coherent theory of learning or underlying body of research. We argue here for such a theory—and for research that addresses the important questions about this relatively new medium that such a theory implies."

i think he's right, but i don't think this abstract stresses enough the cognitive benefits of games. the internet is peppered with studies suggesting gamers' boosted spatial abilities, coordination, and things of that nature. i suggest checking out http://skillcraft.ca/about-the-project/ for an interesting take on starcraft's cognitive rewards. an article examining the merits and potential of the study http://blogs.scientificamerican.com/observations/2011/12/01/how-a-computer-game-is-reinventing-the-science-of-expertise-video/ is also worth reading.

from the article: “I can’t think of a cognitive process that’s not involved in StarCraft,” says Mark Blair, a cognitive scientist at Simon Fraser University. “It’s working memory. It’s decision making. It involves very precise motor skills. Everything is important and everything needs to work together.”

i wonder what other benefits, perhaps currently unknown, interactive media might provide. could it revolutionize education (i.e. interactive textbooks)? consider an mmo where everyone played a member of a town. could this be a highly effective way of transmitting an intuitive understanding of how local economies/politics work? could we view minecraft as a giant sandbox?

TLDR: i think there's a good argument that we do, in fact, get training from games. the entertainment behind it could be a motivation to keep coming back.