Valerie: Oops, you're right, it is Jim (sorry Jim).
We probably all learn slightly different definitions of these "Rules" depending on who taught us art. The Rule of Thirds that I learned about was essentially taking your canvas and pretending there's a tic tac toe board grid on it, that divides your canvas into thirds, both horizontally and vertically. The center of interest (the object that you want the viewer to focus on) gets placed on one of the intersections of the grid. Using this definition of the Rule of Thirds, Jim's leaning tree, specifically the base of it, would be the center of interest, because it is the area of greatest contrast that is placed right where the gridlines would intersect. I don't see anything that would qualify as a center of interest at the other grid intersections.
If we're talking about simply dividing the canvas into thirds, either vertically like a triptych, or horizontally. Sometimes artists start off their piece of art by placing the horizon on one of the 1/3 lines, especially for landscapes. I've heard that called the Rule of Thirds, or alternatively the Rule of Three. Jim's picture is not a good example of that, it's not really divided into clear thirds, as you pointed out.
Just to make things more confusing, the Rule of Three can also mean: including three similar objects in the same picture (the work posted in the thread about Three that Abbie started are almost all great examples of this version of the Rule of Three).