That was a really good video explaining modern economic measures and specifically what it doesn't measure.
I agree with nearly all of it right up until the last 60 seconds when the presenter said:
"If we made iPhones with batteries that would last twice as long, GDP would go down."
The suggestion is that if iPhones last longer, people would by fewer of them and therefor lower GDP would be recorded. However, very little about the economy exists in isolation. So it wouldn't work like that. If iPhones lasted twice as long, which translates very roughly 50% of your iPhone money still being in your pocket, you'd spend it on something else, which would also be counted as GDP.
To illustrate this, iPhones were first released in 2007. Here's the USA GDP charted
Where is the dip in GDP for 2007 from all the money that used to be spent on things other than iPhones? There's no dip because money people used to buy iPhones didn't magically appear in 2007, it was shifted away from things like portable MP3 players, digital cameras, and other non-iPhone-phones. This would be the same thing with iPhones that had batteries that would last twice as long. Money not spent on additional iPhones (because they last longer) would be spent elsewhere negating any loss of GDP.
The presenter does a great job throughout the whole video right up to a couple of those last statements, which soured an otherwise great resource for people to learn.