This case was specifically about whether adding "on a computer" would make something patentable that is otherwise not, but it does have wide implications beyond software patents, including possibly business-method patents.
The things that are by their very existence unpatentable are abstract ideas, and things preexisting in nature (possibly among other things that I am not remembering). This ruling was actually more wide reaching than the red hat article suggested, because it establishes tests specifically to be used in the future and not making it so narrow as they like to do, so that the ruling would only apply to the case at hand.
This ruling doesn't just apply to software patents. The common law rule now is that if anything is not already patentable such as an idea or thing of nature, you can't patent a method based on that thing if the steps of that method are themselves well known or obvious to the industry to which they apply. In this case, an abstract idea combined with an implementation on a generic computer is considered unpatentable, and the precedent cited was from Mayo v. Prometheus where a biological function (i.e. naturally occurring) combined with a common medical procedure to measure that function was considered unpatentable by the same logic. Since Clarence Thomas relied so heavily on Mayo for this decision, that rule now seems to apply not only to stupid software patents, but anything in any industry that seems obvious to those in that industry.
In a way, they did comment on whether specific software-implementation claims would be patentable by pointing out that this claim specifically did not further the state of computing technology, suggesting that software that was truly innovative that did advance the technology and didn't just use methods "well known" and "long in use" may themselves be patentable. Otherwise, why point out that this particular software was specifically unpatentable because it was "well known" and "long in use"?
Interestingly enough, Sotomayor wrote her concurring opinion specifically to make a statement about how she thinks business methods are themselves unpatentable. I don't think concurring opinions have any common law teeth like the primary opinion does, so we don't have any specific precedent regarding business method patents. But we do know how 3 of the justices feel about them (since Ginsburg and Breyer joined Sotomayor's concurring opinion).