He's essentially making Paley's watchmaker argument (i.e. the complexity of a fine watch necessitates an intelligent designer of the watch. Therefore, the universe's complexities like the aforementioned watch necessitates an intelligent designer). There are some damning criticisms of this argument. As Hume pointed out, it is entirely dependent upon induction (drawing general conclusions based on particular past experiences). We can view a watchmaker and see that he has designed a watch. We have experiences with the creation of watches vis-à-vis watchmakers and can say, "Watches come from watchmakers." We can compare one watch to another after its creation and so forth. We have no such experience with the creation of our universe or any other universe, and never will. Thus, its not logical to conclude that the universe was created by an intelligent designer like a car or watch by observing its complexities. Besides that, let's say that there is something to the watchmaker argument. How do you derive from that the Abrahamic, all-powerful, benevolent deity? Underlying Paley's argument is the notion of "like causes of effects (i.e. watchmaker makes the watch, so it came from somewhere. An example from the video was a Lamborghini and we know they have to come from somewhere; universe is complex, someone intelligent had to create it. It had to come from somewhere). This is problematic if you aren't picking and choosing what you want to adhere to and apply like causes of effect uniformly. For instance, if you take the the Lamborghini example, no one person makes an Lamborghini. It's a team effort by many collaborators. Why wouldn't you say it's likely that many Gods created the universe? No one would claim the watchmaker himself as wholly benevolent, omniscient, omnipotent, etc. Why would you say the creator of the universe is?
I think Dawkins has the best criticism of this argument, though. This position conflates the complexity that is a byproduct of living organisms ability to reproduce themselves (and as such may become more complex gradually over time) and the complexity of inanimate objects, unable to pass on any reproductive changes (such as the minute parts of a manufactured watch).