I would dispute the statement that ambiguity and mystery are not a good thing in most parts of human life. Certainly engineering and science are about removing ambiguity and discovering facts, but I think ambiguity and mystery are a big part of the human condition and make life interesting.

As for mystery being an important element, it is one element that can add to an image and make it interesting, but I don't think it's vital, as there are many elements that can make a photograph interesting: patterns, contrast, mood etc.

Because still photography deals with a frozen instant in time, we capture scenes where often there is vital context hidden from the viewer, because they cannot see what has come before or after that instant that the image was taken. That makes the viewer curious and I think is one place where mystery draws the viewer into the photo, trying to make sense of it, answer questions about what is going on.

Another might be abstract or macro photography, where it's not even clear what exactly the subject is. Anything that makes the viewer curious will tend to make them linger over the image longer and be drawn into it more, much like a good movie draws you in to the point you almost forget you're watching a movie, you get so involved with the story.

I don't think it's surprising that mystery is one element that can be important in any art form, particularly photography. I just don't think the comparison to engineering is an appropriate one.