The survey is worded pretty strange. It seems as if you bundle 2 or 3 questions into each category and I don't really see any sort of questions that deal with writing.

When I think of game design, I generally think of the creation of the game design document. This is words and diagrams most of the time and concept art is bundled with it, but even those concepts usually spawn from something written in the game document.

I would say that game design isn't something you can say an artist would be good with, rather than someone who can create or design a good game by means of knowing what you want, how you want it and being able to use creativity along with the knowledge of technical aspects and limitations to design the overall game.

If you have the skills for level design, then you are a level designer, and your designs will generally be created by using the previously made and broader game design as reference.

But is a level designer technically a game designer? Maybe however if you argue that they are because they must be able to make the game enjoyable my using space well that would fit the gameplay, your really just saying that your trying to make a level that is built around the limitations and specifications given to you that tell you exactly how the space is expected to be used for a certain type of gameplay.

At least that's how I see the position of game designer. Overall a game designer's skills don't have to be in being able to use space well or artistic ability. But rather creativity as well as knowledge of the subject and being able to organize it in a manner that other game developers of different types can easily understand what your asking for and start to make the game document reality.

Of course it does help if the game designer also fits into another job because then they can help give actual examples of what they were thinking of for the game design.

Honestly I think that while it may be easy to find a good artist, musician or programmer. It's actually somewhat hard to find a good game designer that can organize a well made game document and really come up with something...well, well designed.