For me I'd say that it is more than we don't know all the variables, but that truly random quantum events can have significant effects. Some local ionization caused by a radioactive decay will, because weather is nonlinear eventually have a significant effect on the weather, and this would affect which organisms reproduce.
I would class it as sufficiently significant if an event changes which organism reproduces.
Similarly, if a nonlinear system (chaotic orbits) caused a mass extinction, then by extension this is also significantly affected by truly random events.
Does that make it clear?