Oh boy, that's not what it says either.
Here is the article:
https://phe.rockefeller.edu/news/wp-content/uploads/2018/05/Stoeckle-Thaler-Final-reduced.pdf
What it actually suggests is this:
Similar neutral variation of humans and other animals implies that the extant populations of most animal species have, like modern humans, recently passed through mitochondrial uniformity.
First of all, they looked at animals specifically not all forms of life. Second, what they are suggesting points to some sort of bottleneck that may have occurred within the last couple hundred thousand years. It does not mean either that all taxa and/or even 90% of animal species came into existence in that time. At best, it suggests a genetic bottleneck of some kind that occurred in populations, and the paper gives various examples of types of bottlenecks that occur.
Nothing in that paper invalidates anything else we already know about origins of various taxa throughout the Earth's history nor the common ancestry of existing species with one another.
Regardless, it's neither here nor there.
First, if you want to make any kind of argument regarding genetic (e.g. DNA/RNA) "information" you first need a concrete, demonstrable definition of information as it pertains to genetics. And this will presumably include a quantifier (i.e. a unit measure) by which information can be measured.
Second, insofar as the "origin" of information in the genome (as per measurements re: information theory), it could be a case of an emergent property of DNA/RNA itself. We already know that chemical compounds can yield emergent properties not explicitly defined in their constituents. And life itself is just complicated chemistry at its core.
I realize that may not be the most satisfying answer, but it could very well be there is no deep mystery to solve. The "information" that we perceive in DNA and RNA may be nothing more than a property of the particular compounds in question.