Could we see their calculations?
Do you need to? This is Hoyle's fallacy, the one using a 747 being assembled in a junkyard by a tornado. The mathematics is useless because the way the problem is set up is flawed even before the first calculation occurs. It assumes that the various biological steps are independent the way that the steps of assembling a 747 would be, and simply multiplies the likelihood of the individual steps to come up with an astronomical number. That's not how biological systems increase in complexity. The steps are not independent, because a process that directs them is involved - natural selection of the most fecund - something the airplane doesn't enjoy.
An analogy would be a planet forming from countless gas, dust, and rock particles. It would be an error to calculate the odds of these pieces finding one another and coming together as it there weren't a directing process involved - gravity. As the planetesimal grows larger, the odds of additional pieces coming to it are increased. And they will form into a spheroid if massive enough under this direction.
Is ID pseudoscience because it brings God into the equation?
It's pseudoscience because it is looking for God. Science doesn't do that. Science looks at the universe to see what is there and to try to identify its repeating patterns. This needs to be done without expectation of finding a god. We know that if one does that, he is likely to "see" what he is looking for - a cognitive bias that deforms the scientific method. And not surprisingly, they kept finding mirages of irreducible complexity, all debunked.
This is a well-known cognitive bias - confirmation bias. It's the problem that is addressed when designing clinical trials and double blinding the patients and clinicians so that they don't "see" what they are hoping to find.
Maybe regular science is pseudoscience because it presumes no God.
It doesn't. Others have told you this on this thread, and I have told you myself. Science does not say that there is no god. Neither does agnostic atheism.
Have you noticed any differences between what is called science and what is called pseudoscience? Let me give you a few examples of each, the pseudoscience coming first in each case: astrology and astronomy, alchemy and chemistry, bloodletting and scientific medicine, creationism and cosmology, creationism and evolution. What do all of the pseudosciences have in common that is different from all of the sciences? The pseudosciences are based in principles believed by faith, such as that the positions of the stars determine personalities and fates, or that a deity made the universe and life in six days by fiat ex nihilo, and that the pseudosciences are all sterile, that is, generate no useful ideas.
The mathematics used in the video seems to point to the conclusion that the regular science presumption of no designer is wrong (from a probability standpoint).
If one can't evaluate himself directly, the mathematics should not be taken seriously if it comes from an apologetics site. Their agenda, methods, and values are incompatible with humanism or science.
In case you want to call that the genetic fallacy, I would disagree. For starters, that occurs when one says the argument is wrong because of its source. That is not what I am saying. I am saying that I don't trust the source and am unwilling to do the necessary fact checking to make an assessment of whether I buy the argument or not. That came home to me when reading some creationist apologetics arguing that human evolution from the ancestors of other extant great apes was impossible, since the other apes all have 24 pairs of chromosomes and man only 23. The argument was that if these other apes had a common ancestor, it could not have been an ancestor of man, since no chromosome dropout mutation is survivable, much less selected for. I happen to have been aware of human chromosome 2, and could rapidly reject the argument, but what if I hadn't been? The argument presented was sound. The conclusions followed from the premises provided. The facts provided could be confirmed, and the subsequent reasoning flawless. Yet the conclusion was false anyway.
It's the same argument for not going to a known or suspected dishonest investment counselor. He makes his presentation, and it seems like a good investment. The facts provided can be corroborated. If he were a trusted source of investment advice, you might take his advice based on that sound presentation. But this guy? Don't even listen to him. And that's not the genetic fallacy, either, since I'm not concluding that he is lying, just that I don't care to find out if he is or put him to the test..