gamers probably make the best developers (IE designers)
This comment made me laugh. I've taken part (as a developer) in lots of focus groups for all sorts of games I've worked on over the years. Gamers in general spend very little time thinking about how to improve games, or even what type of games they want to play. I've heard the absolute stupidest answers to questions on ways to improve the game (for the record, not a good question to ask), and the stupid far outweighs the one or two decent and thoughtful replies that get drowned out.
A very minuscule subset of gamers would be suitable as game designers in my opinion. With that said, I would imagine that most designers ARE gamers simply because usually the best people are ones that are drawn to and consumed by their passion.
To answer the original question, I think that it's important to play games if you are wanting to build a cutting edge experience inspired by what's out there. On the other hand I think a non-gamer COULD theoretically come up with something very unique and interesting simply by not being influenced by what is already out there.