Relaxing for me is thinking differently.
Relaxing can be done many ways, one thing that is relaxing to someone could be a source of annoyance to another, but it's all done for the same purpose. Unwinding, de-stressing, taking your mind off things, relaxing is taking where you were just a second ago and putting yourself somewhere new. Watching a movie, playing a game, reading a good book can all (metaphorically) take you to different places, where you can enjoy a new world's rules and sights for a while and forgetting about your own for a while. Playing games like Portal
("of course I can walk on those light beams. I just can't shoot past the blue energy fields") teach you how a new environment works, with it's own laws and constraints. The upside here is the new environments are usually rich, varied, and entertaining; they stimulate your imagination.
Lots of things to see, lots of things to do
Quick! Run! He's talking about immersion! Absolutely. Exploring the Capital Wasteland in Fallout after classes for the day is great way to relax. I'm the kind of gamer that really gets 'sucked in' to certain games, usually more open ones with a rich world to explore. I can have some fun, feel accomplished, and in the end feel pretty relaxed. Even when attacked or stumbling into a trap and trying to escape, the panic is 'safe' panic, and doesn't stress me out at all (except in most of the Silent Hill series and Creepers in Minecraft). There are exceptions but I find most games are great for releasing stress and relaxing.
What I like about video games, is that unlike any other medium, you really are directly involved. You aren't just watching a character think his way through a situation, you are the character and you have to do the thinking. The Portal games are a perfect example of this. You no longer have to think about bills or work or whatever it is that's weighing on your mind. For a while, you have to think about how to teleport cubes across chasms, where to paint walls (and what color) to reach floating doors, funneling laserbeams through dimensions unknown to press buttons. In most people's daily lives, they don't have to think about things like these (if you do, I'd like a job doing what you do please). Playing a lot of games, though, I am used to thinking in different ways and can unwind looking back and figuring out a test chamber, whereas 'non-gamers' may get stressed at the mechanics or constantly worry about controls and handling character. The more comfortable you are with the mechanics/game world, the more relaxing the actual gameplay can become, you can focus purely on working out solutions. It's like math (using your brain in creative or new ways to arrive at solutions), if math was about shooting digital space soldiers in their uncanny-valley faces.
Shootin' the breeze...err, Pyro.
Team Fortress 2 is another great example. At its most basic, you are choosing which weapons to go shoot others playing the game with and then doing so. Without getting into the ridiculous 'game violence is bad' thing, that alone is relaxing on one level for a lot of people (just look at how many play COD). Then, going deeper, each class has its own distinct personality and with that, a set of dialogue. Together on the extremely well designed maps, it really gives a sense of fighting on a battlefield with other unique personalities. The context sensitive nature of the lines really adds to the experience, random unique dialog lines spoken in situations I can only guess at (streaks, close calls etc). Each time that happens, it's usually right after I have pulled off some sort of nice move, and it's almost a reward that brings even more personality into the game. From the scout's patronizing laugh when you pull of a nice kill, to the giant laser guns on top of the BLU bases, everything is 'believable' in the context of its own world - a place I can go to where I can relax and build some sentry guns.
I could talk TF2 for a while, but it's not the only game or type of game I find relaxing. There have been quite a few games especially in recent years that seem to put the focus on tranquility. Games like Flotilla, a minimalist space combat simulator with a soundtrack of classical piano, the ever-popular Flower, the upcoming Journey and the simpler games such as Fl0w put an emphasis on peacefulness even if you are doing something as chaotic as blowing up space ships. Just like how people choose different genres of movies to watch based on their mood, so too do I choose between types of games (subdued, frantic) depending on how I feel like unwinding. Most days of the week last school year, I could come home after classes and find my housemates on the couches playing Halo. It was great to relax and maybe have a beer or three while blasting bad guys (there was even a daily achievement which was called "Blastin' and Relaxin' ") before getting down to some homework. Getting these quick rounds in was a great way to take my mind off things temporarily, but on busier days where I'd be in the library or a lab all day, coming home and playing some DEFCON or Braid couldn't have felt better. After all, for me relaxing isn't about not thinking, but rather thinking in different and challenging ways, which is why I am and will always be a gamer.