I could not find a reliable source for an exact definition, so here is a collection of references to explain how we understand this use of "to be the less for".
The Oxford Dictionary has a possible definition labeled as Archaic here:
Of lower rank or importance.
‘James the Less’
This conversation better defines "the less for" as "to be diminished" and references the first usage in 1624, a poem by John Donne (spelling edited from original writing):
...if a clod be washed away by the sea, Europe is the less, ... any mans death diminishes me...
This compares how a small piece of dirt lost from the land of Europe makes Europe smaller (size, value, quality), and how any person's death makes every other person smaller (size, value, quality).
It isn't completely archaic, there are some examples of it still in use today (bold added).
From The South Ellis Island:
...when our refugee neighbors flourish, we flourish. When they do not have the opportunity to bring to our community the full force of their ambition, we are the less for it, our families are the less for it, and the city is the less for it.
This basically says "when our neighbors get better, we all get better. But when our neighbors are ignored, we all get worse (or at least not better)."
From this article, about a woman's death:
She was an enormous gift to our community and she will be missed. We are the better for her all too short presence amongst us, and we are the less for her passing.
This demonstrates the opposite phrase "are the better for", showing that "are the less for" does mean "a worse quality or state". Today this is often where I hear the phrase, when speaking about someone's death as lowering a community's quality because that person made the community better while alive.
So the quote about Columbus
The columbian exchange left us with not a richer, but a more impoverished genetic pool. We, all of the life on the planet, are the less for Columbus, and the impoverishment will increase.
The columbian exchange did not improve the diversity of life, it made it worse. All diversity of life on the planet is worse because of Columbus and it will continue to get worse.
I'll let the video explain why the quote says that.