While there are several problems with the challenge, the disguised religion comes around the 1:15 mark, shown above, where the criterion of homology is explained. Don't worry if you are not familiar with the concept of homology. The bottom line is that the challenge uses random design as a test for whether a structure evolved. Specifically, if there is any non random pattern detectable, then it must not have been designed; instead, it must have evolved.
This is today's version of a test that dates back to Daniel Bernoulli and Immanuel Kant in the eighteenth century. The idea is that God would not design according to a gratuitous pattern. If a design is not physically required, then God would not use it. Instead God would exercise all the possible variations in a design. As Kant wrote (concerning the design of the planetary orbits in the Solar System):
Thus, God's choice, not having the slightest motive for tying [the planetary orbits] to one single arrangement, would reveal itself with a greater freedom in all sorts of deviations and differences.
Laplace and Darwin both relied on this argument. For instance, Darwin argued that if God created the species then we should find "a sudden leap from structure to structure?" As Darwin pointed out, "We never find the bones of the arm and forearm, or of the thigh and leg, transposed." Today this argument is ubiquitous in the evolutionary literature. But it appears in shorthand, such as in the above video, so as to disguise the religion.
Those interested in the details can read more about evolution's religious premises here and here. The bottom line is that a crucial evolutionary premise is that observable patterns across the species disprove independent creation and mandate an evolutionary origin. The YouTube video is yet another example of this, now commonplace, metaphysical logic. The argument may appear to be scientific, but this is merely a disguise. The argument does not come from science, and it has no scientific justification. It comes from personal metaphysical belief that is fundamental to evolution.