“Are you saying that as long as you descend from the Avos, having other gedolim along the route is irrelevant?”
No. (although I agree that boasting is childish – even worse, it demonstrates bad middos and shows that the yichus is meaningless since the person clearly did not inherit his ancestor’s middos.)
“Or are you just decrying the condescending attitude of Yichus?”
That was probably part of it. I think it was more about reminding people that being descended from the Avos is the greatest Yichus, so even if someone does not have “yichus”, they should realize that they actually have the greatest yichus.
When it comes to the Avos, it is about zchus avos which is based on the fact that the Avos are out “shoresh” and all of us have inherited their qualities and therefore have the potential to be like the Avos (which is why we are supposed to ask ourselves, “Masai yagiu maasei l’maasei avosai?”
When it comes to other Gedolim, I don’t think that is necessarily the case.