Creativity is all about the element of surprise.
The goal of creativity is to put players in a scenario they haven't been in before, solving a puzzle unlike anything they've seen before, and reaching a goal they've never reached before. It's pretty rare to find a room that can do all of those things, but that's the goal of creativity. Those of us who have played a lot of rooms just want to say, "I've never seen that before."
For example, even though people love prison themed rooms, prison rooms almost always lack creativity. You start by finding or assembling a rod with a hook to bring something close, reach a key, or give something to a teammate locked in a different cell. There's almost always something behind the mirror, under the mattress, and in a drain.
It takes a lot of creativity to integrate a puzzle into the environment, but when it's done well, it's very exciting. One of my favorite surprises was when I did a room in Kansas City, and the entire room was unexpectedly upside down. Consequently, you had to flip over most puzzles to find the solution.
The element of surprise comes when a drawer, bookcase, picture frame, floor panel, wall, or something else unexpectedly opens. It comes when a black light reveals a giant mural on the wall, a dead body moves, or smoke reveals a laser. A great room includes at least one wow moment, an element that's worth telling your friends about.
I recently did a room in Las Vegas with live actors, and the most creative aspect of the room was humor. The actors literally got me laughing out loud multiple times, and that's not easy to do. When I'm in a room, I'm intense and competitive, and I was amazed that the planned jokes made me laugh.
In my opinion too often game designers put the wow moments too early in the room. Some designers attempt to create excitement at the end of a room by concluding the room with many simple puzzles, and that does work to help the players leave the room with some excitement, but rarely am I surprised at the end. For me, a wow moment at the end of the room leads to better memories of the entire room. My theory is that game designers don't do this because some teams don't complete the room and therefore miss the surprise. That's why I'm a big fan of unlimited hints. When it becomes obvious that a team is going to lose, I think a game master should offer enough assistance to at least get every team to the final puzzle.
That leads me to competitiveness.