"Evolved to Extinction" because female mice become rarer and rarer? "Female mice become rarer and rarer" is another way of saying at least 50% of all the genes in all the female individuals will make it to the next generation. Which is pretty damn good odds. Consider all the mutations in all those male individuals that will never get a chance to make it to the next generation, because the male individuals will never even get a chance to get close to a female, much less mate with one.

But the male chromosome isn't competing against the female chromosome. The mutant male chromosome is competing against the unmutant male chromosome. The mutant male chromosome is fitter, rises to fixation at its allele location, and in one more generation the species as a whole goes extinct.

Even if we decide that "evolving to extinction" should not refer to any case where environmental conditions change - and I think it's fair when the environmental conditions change as a direct result of the evolution itself, rather than exogenously - it is still possible for a species to evolve to extinction directly.