"Creative individuals alternate between imagination and fantasy at one end, and a rooted sense of reality at the other".
This sentence is a good starting point. I feel it is the core definition from which to build upon. There are many defining characteristics of creative people yet it lies in all of us; for those who can use their imagination at least.
It is a characteristic that is applied in many ways. Often associated with art & graphics and the likes, yet it is prominent in so much more than that. The 'creative industry' just has a lot more freedom because that is its speciality.
Intelligence and mental health have been connected to 'theories' of creativity, so to speak. It makes sense that the more you know about the hows and whys of the world, the more plausible creations you will produce. As for mental health, manic depression has been present in famous poets, writers and artists. This may have affected their work in a strong emotional or delusional way, I can't be sure.
There are so many ways to look at the term creativity, from originality and level of detail to efficiency and design etc., and these all have different levels of importance depending on what the situation calls for.
Creativity can produce nothing of worth yet this world would be nothing without it. Without the desire to create, how would we progress as a race?
Because creativity is often adressed for its uniqueness, games described in this way are ones that appear to think out of the box, even if marginally. It can show itself through any aspect of producing a game - colour design, characters and how they move, narrative and so on, yet they are rarely all unique in one game alone.
Technical constraints are an issue but not neccessarily a bad one. They force us to find another way to think, another way to solve a problem. Many creative people are acknowledged so because they think differently and in the Game industry it's a sorely needed breath of fresh air.