This answer can hopefully be useful as an additional perspective on top of the existing ones.
Note that the spectrograph is a plot of (the log of) power output vs frequency (power being energy per unit time). I would say that the total power in the peak at 82 Hz is quite a bit more than the total power in the peak at 247 Hz. The peak is broadened and thus the total power has been spread out among surrounding frequencies and the central peak maximum is somewhat lower, but if you plotted the integrated power for each peak in a window of plus or minus 10 Hz, the 82Hz peak would, I think, clearly be dominant.
There are many reasons why this may be, which could depend on, as others have said, things like where and how you pluck the string, how the other strings and the body of the guitar resonate, and the actual composition and behavior of the string itself. The key point, however, is that the "fudamental frequency" (82 Hz) does, in fact, contain the majority of the power output, but that strings do not actually act like a perfect, ideal string treated in an elementary physics course. There are non-linear corrections to the perfect string behavior which depend on the actual tensile properties of the string (ideal strings do not stretch, for example), as well as the resonant effects of the other strings and the body of the instrument, all of which contribute to the "timbre" of the instrument and contribute to the rich sound. While for a perfect string one would expect perfect peaks at multiples of the fundamental frequency (delta functions for you math nerds), all of these complicated, non-linear corrections contribute to the broadening of the peaks, and how much each peak broadens depends on the frequency (which we physicists call dispersion). In this case, it appears that the fundamental frequency peak is strongly broadened, while the higher frequencies are much sharper, so the low-frequency modes are much more dispersive than the high-frequency ones (this is also why you have the broad continuum background at low frequencies which tapers off at higher frequencies). Perhaps others can speculate as to what causes larger dispersion at lower frequencies.