I have not watched that video yet but I have also done the math and agree that the monk is way back on where it should be. The monk is only competitive if it gets flurry of blows every round.Chaosmancer alluded to this, but I just watched the Deep Dive into the UA Rogue, and at about the 45 minute mark when comparing damage from the updated classes, he brings up the monk. It's terrible - at level 13 even when using Flurry of Blows the monk is doing less than half the damage of a berserker barbarian, and about 60% of the damage of a fighter or rogue:
He also explains why weapon masteries are currently useless to the monk; I know a few people in this thread have suggested the opposite, so here's the math if you want to review it.
Long story short: the UA monk is in dire straits and we need to make that clear to WotC when the survey comes out. The good news is that the first version of rogue was widely panned, and this latest one is massively improved, often specifically addressing complaints and suggestions from the community. So there is hope!
My initial analysis does not take masteries into account, but the UA monk is about par with the 2014 Warlock base up till level 10 or so and left in the dust after that. It is an improvement over the current monk (IMO) but heavily dependent on getting flurry of blows off. I think it should have an automatic nick like extra unarmed strike built into the base martial arts.