No, they have nothing to do with how good he was at chess. That is the point.
True, the two have nothing to do with each other. However, they are both equally relevant when considering a person as a whole person.
So, viewed as accomplishments outside of drawing and scribbling in his notebook...that's all his genius amounted to. An alternate bridge support, and a temporarily useful way to wind bobbins and grind lenses. Thus, I think that judging by pure accomplishment...it's pretty easy to discredit intellectual achievement.
You're not understand what I'm trying to say. Perhaps I'm not being clear, so I'll try a different approach.
Let's try to quantify things to make them easier to understand. I'll propose that people, over a lifetime, develop a reputation, and we'll measure that reputation with units that, for the sake of this argument, are called Cool Points.
Bobby Fischer, by winning a World Championship while simultaneously being American (certainly no small feat when it comes to chess, considering it's only been done twice), against the Soviet Union in the middle of the Cold War, earned an incredible +2500 CPs. However, by turning around and bashing his country (Death the the US, the US must be destroyed, etc), denying the Holocaust, and publically advocating genocide, Fischer earned -2950 CPs. The result is, Fischer's reputation is -450 CPs, an overall negative total. One can certainly acknowledge that Fischer was a good player
and consider his achievements when calculating his reputation, but - and this is the underlying theme of my objections here - those achievements
aren't enough to get Fischer out of the red.
This applies to Da Vinci as well. Perhaps you're right, and all Da Vinci has is his intellectual achievements. But Da Vinci is different from Fischer, in that he has no huge CP deficit to dig himself out of; those intellectual achievements are not overshadowed by anything atrocious, so Da Vinci skates to the finish line.
And this certainly isn't the first time in history that a person who, after a lifetime of accruing many, many CPs, made a few mistakes (or even a single mistake) which just totally negated them all, and then some.
Now, perhaps one could argue that the CP values I've attributed to Fischer's actions are completely arbitrary. Well, that's certainly true - we're dealing with reputation here after all, of which the observer's personal views and politics are a dependent variable. You could argue that you think Holocaust denial, advocating genocide, and etc. is only worth -300 CPs, putting Fischer clearly over the top. When we simplify things in this way, we find that what we're really arguing over here is whether chess is more important than personal humanity. I feel that it isn't. Your mileage may vary.