The antithesis of algorithmic thinking is instantial thinking. There's a lot of instantial thinking in many of the products being designed these days, and it always leads to poor designs. The instantial thinker works with specific cases rather than broad generalities. He comes up with great cut scenes, but lousy interactions. When he designs an adventure game, he loves to cook up strange dilemmas in which to place the player, but the idea of a dilemma-generating algorithm is lost on him.
Any storyteller needs to be good at instantial thinking.
The problem comes when good instantial thinkers attempt to apply their skills to interactive design. It doesn't work. Sadly, algorithmic thinking is so fundamental to a person's outlook that I do not believe it to be a readily acquired skill. I've wasted a lot of time trying to help people think in more algorithmic terms, and I see little progress in mature individuals who are not already inclined in that direction. By the time you're 20, either you've got it or you don't.