First thought is this. The video is put out by the Discovery Science News Channel, the official Youtube channel of Discovery Institute’s Center for Science & Culture. The prominent leaders of this organization are supposedly fine with the conventional geological record, dating, common descent and evolution, just not “Darwinism”.
Discovery Institute affirms common descent. Whales obviously did not descend from spiders or birds. They are mammals. They descended from ancestral mammals. So what is DI’s problem? The video is talking dating and the fossil record here, not irreducible complexity.
Discovery Institute affirms evolution. Not in the mainstream sense of course, but with some divine design that progressively nudges the species along as opposed to instantaneous, ex nihilo “poofing”. So we have a fossil record which shows exactly that kind of progression in remarkable detail. Again, what is DI’s problem?
So if a vigorous rebuttal of this video is desired, I would suggest that it come from an organization that supports common descent and evolution. If the Discovery Institute means what they say, ask them.