I'm not going to read all that at 4am (my sleeping pattern is fucked, doing night shifts and housekeeping) but from the brief glance I took, it seems that study was observing female dolphins and their behaviour during estrous, whatever that is, presumably the dolphin term for "in season".

Inbreeding bad, leads to bad things.
There's no dispute here.

Ergo, animals that do it will die off
This is in dispute. Why would they die off? Presumably the implication is that incestual beings are only fucking their family members. First of all, this happens when populations become too small, and that might or might not mean extinction, so it's not a given they die off. Secondly, this assumes that incestual beings are exclusively incestual, that is they aren't having non-incestual relations. But that isn't the case. In most cases in the animal kingdom, incest is also rape. It's sexually aggressive males doing what they want to do, and submissive females accepting it, or weaker males hating it.

and animals that avoid it will survive to pass their non-incest-doing genes on to the next generation.
Again, implying it's exclusive, that it's a "preference" in an individual caused by a gene, rather than a simple behavioural response to hormones, coupled with a lack of morals and empathy.

We're probably the only animal on the planet that has figured out it's bad. If dolphins give no fucks (and yes I appreciate I haven't shown it to be definite), then I'd be surprised if any other wild animal has the intelligence. Maybe some primates have figured it out.

I could be wrong of course, but it's not how I understand evolution. Evolution is a product of chance. Incest isn't a product of a genetic mutation that will ultimately get weeded out of the gene pool. If it was, it would only happen very rarely. Normal sexual behaviour is more likely to result in reproductive success than incestual, so an incest gene would get weeded out of the gene pool. Clearly that hasn't happened.