What do you bet that this guy paid a lot of attention to unsprung weight on his cars? Speaking of that, of course it's not only rim weight, but tire weight also which should be considered. Using his own aero wheels in this experiment is an absolute no-no, taking away all credibility.
That nitpicking aside, the data files supplied are much too coarse to be useful in making the kind of statements this guy made. To see any rotational weight differences, one would have to look at data intervals on the order of tenths of a second or finer. What's not being considered is the minor accelerations which happen with every pedal stroke, especially when standing. Of course the energy put into the wheels by tiny power variations comes right back out again because momentum. However it takes a tiny bit more muscular effort to accelerate and decelerate than to maintain an absolutely steady speed. It's probably possible to take these micro-efforts into account if one had sufficiently fine data and knew the exact physiology of the particular rider, but of course no one's going to do that.
I think we could say that over the decades, riders have decided that light wheels climb better, using only their subjective feel for it, much the same as that light bikes climb better, even if the computer says there's only a few seconds of difference for that little bit of weight. In both cases, it could be that the act of rocking the bike feels different with lighter wheels and a lighter bike, For sure even I notice large differences in weight, just by feel, therefore small differences must be there, too.
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Results matter