Well, actually the wobbles cause climate variations, which in turn spur evolution and extinction. According to the researcher, who specifically points out this cycle is on the order of millions of years but notes that other cycles can occur on smaller time scales.
They also give voice to a critic, who says that the sample size of species is too small to draw this conclusion, and that any noticed pattern is just a coincidence, noise in the data.
Which is exactly why I'm often skeptical of this variety of research. Interesting, yes, and you can draw reasonable conclusions. However, this isn't the kind of research where you can run multiple trials and verify your data. You're looking at historical aspects and data derived from biology/geology/astronomy etc. records. The questions there are usually focused on how you obtained the data and whether or not you're interpretting it correctly.
The only reason I keep skepticism of the research is that with such a limited sample set (we only have one Earth, after all), it's hard to determine whether or not someone is interpretting the data properly.
Oh well. I'm a biochemist. What would I know about orbital cycling and its effect on the climate and speciation?