If I had to guess, I would say that the one on the right went through Photomatix, but the changes I see could just as easily been caused by a slight change in the pattern of dappled light falling on the sign.
The most prominent change I see is that the bright spot on the lower left of the sign is well controlled in the RH image, but completely burnt out in the LH image. Also, the brightness of the red lettering on the RHS of the sign is also more controlled in the RH image, but because the shadows caused by the light coming through the leaves of the trees, these observations could be completely unrelated to the use of Photomatix.
To be honest, I'm not sure what this was meant to illustrate. In fact, I would say that it's a potentially misleading representation of the typical uses of HDR. There are at least a dozen adjustable parameters in Photomatix, so one can set it up to do almost nothing, or, just as easily, set it up to wildly compress the dynamic range of a scene. In addition, the strong, and, IMHO, completely unnecessary oversharpening of the image obscures changes introduced by Photomatix's algorithms, and only detracts from the artistic merit of both images.
IMO, below is a much better, and much more typical example of the type of changes introduced by HDR tone mapping algorithms. The 1st image is the best conventional, single exposure of the scene, whereas the 2nd image was produced by feeding Photomatix with 6 exposures of the same scene, spaced one stop apart. No further processing was done to these images except down-rez'ing for posting on the forum.
Note that after the HDR process, the deeply shadowed side of the more distant chair is much brighter and details are now easily seen. Similarly, the complete lack of detail in the overexposed area of the blinds (just above the arm of the distant chair) in the conventional shot is completely fixed in the HDR version. These are two examples of what tonal range compression is supposed to do.
Tom