Assuming they produce viable offspring, isn't that one of the primary definitions for a single species?
It is one of the definitions, yes, but not the only one. And while it's true that inviable offspring show that there are two separate species, two separate species will not necessarily produce inviable offspring.
Darwin's finches in the galapagos are commonly used as an example of an evolutionary speciation event, but they are able to interbreed and produce viable offspring. What counts in this case is their reproductive isolation: they don't normally interbreed.
Reproductive isolation can result from differences in appearance, geographic location, breeding rituals, or other factors. These factors may then result in the separation of species.It all seems like a bit of a crock to me, but the definition of species appears to be a hard problem.