Somebody asked me recently "Why do you make games?" I actually had an answer, and it is based on the idea that the nature of games has obvious implications for the nature of playing games, and thus affects the nature of making games.
First, let's define Games. Eh, scratch that. Instead, let's talk about what games are about. It might seem like a semantic difference but for me it's really important. If you define game as "a set of rules with a goal etc", or "a feedback loop of bla bla bla" then you are, by literal definition, missing the point. Games, video or otherwise, are about exploration, education, and social interaction, and have been for millennia.
The Unique Properties of Game are interaction and feedback, in some form or another. This is what distinguishes Game from Pasta, or Movie, or Car (actually cars are a bit like games, aren't they?). These Unique Properties mandate that the first core quality of Game is exploration. Not in the Vasco da Gama sense, but in the experimental, Montesourri sense. You give the system input, it gives you output to let you know what your input did. This is the basic process you engage in, whether you're playing Backgammon or Solitaire or World of Warcraft.
Education goes hand in hand with exploration. It is a necessary process for altering and updating your internal model of how the game system works while you explore it. "Oh, I played a Spade that time, and lost. Noted." This might seem really obvious, but I am enamored of the apparent fact that this is not something that some games have; this is something all games (again, video or otherwise) have by default. If you can "play" it, then you are inherently exploring and learning. You might not be learning things that apply anywhere in this universe except to this particular game, but these are the core processes implied by the Unique Properties of Game.
These properties are not just limited to human games, either; they're pretty universal. Dogs play fight to learn their limits, explore who is dominant, and to interact with each other. I think we play Poker and Football and Street Fighter for all the same reasons. Even if it is a single player game, you still talk about it with your friends; it becomes part of your social framework for relating and empathizing with other people. Games are an excuse and a conduit to interact with other people. While you're a child, games are your whole way of relating to the world. When you're too old to work anymore, your social life migrates toward games again; lawn bowling and bridge are a way to meet people and relate.
I think this is more interesting than defining what games are. All three of these qualities are near and dear to me; I love to explore and learn things with my friends (this extends in a meta way to the game dev community even). But they have a lot of interesting implications that overlap my other areas of interest as well. If your medium thrives on or encourages exploration, that means you have to create something to be explored. I see games as a mandate to give players more questions than answers.
Hold that thought for a minute. Everything I've typed so far applies to all games ever created by humans or animals in recorded history, and probably longer. These are simple, essential qualities of "stuff with which you interact." Passion for these subjects is why I am obsessed with designing games. So why do I design video games, and not board games or sports?
My oldest answer to "Why do you make video games?" was something like "Well, I played a lot of video games growing up, and just want to make games." This is true, and is part of the whole truth. Nostalgia plays a role in my attraction to the form.
Then, I started to rationalize it and make it more academic: "This is the mixed media form with the lowest barrier of entry, and it is new enough that there is a lot of space to be explored." This is also true, and is also part of the whole truth. I adore mixed media, whether it's comics or movies or theater, but these things have been around for more than a hundred years. I am drawn to video games because they are a frontier; I can stay inside with my laptop for a weekend and make something that influences a lot of people. For me, this is hard to do in comics or film.
But now I've realized that all of these things: nostalgia, mixed media, and unexplored territory, these are all specific to video games, and are ancillary to my basic compulsion to create things that people can choose to explore. More than any other medium or art form, games require you to create something abstract and open to interpretation by their very nature.
I don't for a minute think that this means video games have to be "nonlinear" or literally abstract in an audio-visual sense in order to be a Game. I certainly haven't made any games like that, though I do enjoy them immensely. What I do think this means is that games are the best place for mysteries. And to be clear, I don't mean mysteries in the Miss Marple or narrative sense, even, although those are good too. I am simply talking about questions that don't have answers right away. Games are the place where the audience can finally scratch that itch.
Make something itchy.