> But what if there was a way to write algorithms that can't be expressed with a von Neumann architecture?

There almost certainly isn’t, due to the universality of computation (see the Church–Turing hypothesis). At any rate, even if this hypothesis turns out to be false (almost unthinkable), DNA won’t offer anything beyond what classical von Neumann architecture offers.

> Do you think someday that biological computing could perform useful computations?

Potentially: proteins are a good potential starting material to build nanomachines. However, this has got nothing to do with this article. As the initial comment said, the article is completely unrelated to biological computing platforms, the title is pure clickbait.