Before I got a job, I played games a lot, on some days eight or ten hours a day. I still try to spend a significant amount of time (a 'serious' amount) on any one game I'm playing, and to play it in chunks of time eight or so hours long, if I can string together that much time consecutively (normally I can only do this on a weekend). If I don't succumb to malnutrition or warp my spine what I'm rewarded with is a dream or two related to the game that night.
What's the utility of a dream? Everyone has had the experience of writing a piece of code, or working on a math problem, or playing a game, or reading something, and having difficulties with it- and then, hours or days after giving up in frustration, have the solution to their difficulty (or, at least, a novel approach) appear spontaneously. Dreams are just a more radical and immediate form of thinking-by-separation, when you're churning through the problem you just confronted, but at a more leisurely or casual pace and with less anxiety (the book with the imposing derivations, or the bracket-bound code, isn't right in front of you). It's perfect for reflection, even if that reflection (in a dream) is warped.
More practically, what I noticed in my dreams about games is that the things which I did most often and the pattern into which my actual playing of the game fell would be revealed in a much more obvious way. Playing Max Payne, I didn't really notice that most of my time I was sliding to the side in slo-mo. It was happening at a level below whatever my engagement with the game was- I was thinking: 'here is an enemy, I'm getting rid of him so I can reach the next room' and sliding sideways was an automatic response to that imperative. Having a dream where all I did was slide everywhere sideways with my arms pointing out made it much more obvious (and funnier) than the action would have been otherwise. I remember a dream of Anno 1404 in which I felt like I was constantly moving closer and closer to the corner of a house (from a birds-eye isometric viewpoint) without ever passing through it, and where it felt like the corner of the house was growing more and more magnified until I was staring at a single knot in a single board of wood. This reminded me to stay back from the monitor a bit, and also reminded me that all radii city-builders (city-builders where service buildings etc. provide services in a fixed radius, as opposed to the walker system which I think is more organic) turn you into a surveyor.
Another example of a game dream is actually the youtube I posted at the top. I remember playing Serious Sam for a punishing amount of time and getting dreams in which I was eternally running backwards, firing into a flat wall of weird faces. It seems someone else either had the same dream or the same insight. And with this sort of thing the journey really is irrelevant- getting there is way more important. Please don't play games for ten hours a day. Sweet dreams.