At the end of the 30 years, the buyer in the video would not own the house. He would still owe $1M in order to own the house (if the market is good, the house could very well be worth more than $1M, but that is besides the point).
The amount that he was paying monthly goes towards paying off interest on the loan, property taxes, etc. only.
I agree, as others have pointed out, that the exact numbers differ based on location as well as situation (mortgage size, etc.) and in some cases it is better to buy vs. rent.
However, I think it was a good video because it does an apples-to-apples comparison and clears up a misconception that many people have about buying. In part 2 of the video he sums it up pretty well "You are not a home owner until you have no debt. Until then, you are a paying rent on the money you owe instead of the place you live - you are a money-renter".
Evident from the comments here on HN as well as the blog post, many people mistakenly believe that monthly payment in a buying situation all goes towards equity or "savings". But after 30 years, the buyer would still owe $1M on the house - he hasn't saved any money at all. Reading some of the comments, it's almost scary that people about to spend a huge amount on a home don't understand this!