The maker of this video does give the disclaimer that the video is not intended to cover the topic of abiogenesis. I’ll take a bit of a whack at that to add to the completeness here. The argument that the watch proves the watchmaker goes like this. If you’re walking on a sandy beach and you see a watch, you can assume that someone made the watch. This is a fair bet for the normal circumstances of our lives, but is also a strawman.
If you are walking on a beach made up of billions of watch parts that are constantly being churned by each passing wave, and if the watch parts have the natural affinity for each other that the chemicals of life have and if a sufficiently simple enough segment of a timepiece, even if it cannot tell time, can reproduce, and that telling time to any degree conveys an evolutionary advantage, then after some number of millions of years, I would expect to find a beach littered with watches of various styles and types and even some clocks and grandfather clocks.
All analogies are just that. However, as pointed out in the video, this is the analogy chosen by creationists. This second paragraph is a far more accurate analogy to life on this planet, while still being just an analogy. However, remember, the watch parts (actually amino acids in the real world) have recently been found in comets. So, the early solar system did already have the building blocks for life in sufficient quantity to show that the beach made of gears and springs and such is a far more accurate analogy to the early earth than a sandy beach with a lone watch on it.
For those who missed the news of the amino acid on a comet, here’s an article in New Scientist.