I don't want to strawman anyone. Are there really Anachrocapitalists who believe that the market should decide whether or not we have mass extinctions, or is this post mostly satirical?
There are so many problems with this idea, not the least being that markets aren't designed to eliminate niche ideas, they're designed to support them -- and because wild populations of elephants are a shared common resource, even a small number of people who are happier owning tusks means that their preferences suddenly outweigh the vast majority that want them to stop killing elephants.
Markets aren't designed to stop people from irreparably damaging commons and messing up the world for everyone. That doesn't mean markets are bad, it just means... that's not what they were ever designed to do. You're using them to try and fix a problem that they're not optimized to fix.
This is very much a, "if all you have is a hammer, everything looks like a nail" proposal. We don't need to solve literally every single problem with Capitalism. We especially shouldn't look at every single problem and say, "Capitalism doesn't solve that, so it's not a real problem."