And I guess you didn't too. I watched the teamfight at 44 minutes, and you cannot even deny the fact that ezreal missed like 9 out of 10 mystic shots, while his team did mostly everything. The ones he landed did like...100 damage at most. He just racked up kills.
Not to mention that caitlyn got pretty much destroyed by gragas before the fight started. Then at ~47 minutes, he didn't kill a 100 hp lee sin(granted he shielded), with 1 mystic shot, 1 arcane shift and 2 autos.
Then he steals baron with a well timed ulti, that has nothing to do with his build, and the other team, already behind and without the baron buff, get aced.
So yea, I watched some of the fights in the video. This video proves that the build works "ok" on ezreal, but I didn't see him doing anything miraculous worth mentioning.