This is an ongoing problem I encounter in my work as a game designer - a lot of people, even in the industry, and even students well into game design programs themselves, don't understand what designers do. XD
So the term "game design" gets applied very loosely among gamers, developers, educators, and game media alike, serving as a catch-all for "doing stuff that contributes to a game" rather than clearly identifying its own specialized discipline.
The best definition I know is Liz England's The Door Problem, with its extensive array of examples of design problem solving, though that's hard to boil down to an effective tag summary. ;)
I think Pikalek is on the right track in focusing on decisions and rules. I'd be inclined to lead the summary with something like:
Game Design is the process of deciding the rules and mechanics of a game, and balancing them to achieve the intended play experience.
That last bit about having a target experience in mind is important - design is conscious creation. "Creating something without any outcome in mind is not design but experimentation" as Lehdonvirta and Castronova put it.
This also echoes Salen & Zimmermann's "The Game Designer only indirectly designs the player's experience by directly designing the rules"
I think the remaining tag summary should probably warn off common misconceptions, that the tag is not for questions about programming implementation/architecture or visual art / character design.
In the tag wiki I'd want to guide users toward asking well-structured design questions, because it's easy to stray into "too broad / primarily opinion based / unclear what you're asking" territory with these questions.
Taking a look through some of the better design questions I've come across in my time here...
- Establish the context of the game in which the feature exists (genre, single/multiplayer, related features)
- Explain the feature or mechanic whose design the user is struggling with
- Define a desired outcome, or a problem/undesired result to overcome
- Ask for strategies to adjust the rules or balancing to achieve that outcome
Which I think suggests a template worth providing for users who click into the deeper tag wiki (or to which we can link users who clearly didn't read the tag wiki and need help tailoring a clear, on-topic question)
Other types of design questions I've seen handled successfully:
Asking for definitions and clarity surrounding game design terminology (eg. What are affordances in game design?)
Asking about the rationale for common game mechanics (eg. What is the purpose of having lives?)
(This last one I see as particularly high-risk for veering too broad/opinion-based, but it's led to some good Q&A in the past in some cases... I'm not sure whether there's any particular guidance to offer to help tailor these)