I've also written another couple of design columns for Kobold Quarterly, which you can read here and here. I'm not at all loath to promote these when they come up, and I'm entirely willing to take suggestions for columns.
When I write or talk about games, I like to have some common foundational knowledge for the discussion. To that end, I'm partial to the definition of formal elements of games outlined in Tracy Fullerton's excellent Game Design Workshop, though I modify it slightly. Based in part on the work of Salen and Zimmerman's Rules of Play, these features include players, boundaries, rules, procedures, objectives, resources, conflict, and uncertain outcome. I'll be getting into each of these later. Why these and not a different definition? In part, because this is a quickly functional definition that allows people to understand what we mean when we talk about games, and in part because I don't think the definitions that delve into semiotics and the study of meaning provide any deeper insight.
Games are primarily functional tools, and while it's valuable to study their place as cultural artifacts, it doesn't help us to understand how to design and play them with any greater clarity. Certainly, one could study Ian Bogost's Cow Clicker as a satire of the Farmville-style "games"; in this instance, we do benefit from a more analytical approach. However, as JE Sawyer of Obsidian said in a related discussion:
When academics deal with people who are part of a creative industry, they have to understand that many of us are actively attempting to solve problems that are right in front of our face.
It's important to remember that games are more than a collection of formal elements. They also combine, and indeed require, dramatic elements to help bring these formal elements to life. It's entirely possible to make a meta-game game wherein Player seeks Resources to gain the upper hand in Conflict in order to achieve victory in Outcome, but that's hardly a compelling story. Instead, we need to put a new framework on what is essentially a formalized skeleton.