I don't know when the video was taken from the Prius, however, modern 2017 and 2018 models use Lithium batteries.
I think Shouty knows about as much of priuses (or more) than me.
And that would probably include, that many EVs (hybrids) use their large battery pack to start the motor in case of start-stop.
Not all of them.
If the Prius is anything like the Tesla, the 12V battery is used to power the electronics in case of a depleted battery pack, as well as use the 12V to start the engine in case it is depleted.
I can admit I don't own a Prius, and don't know much of it, but reading from the post below, it appears to me that the Prius mainly uses it's battery pack to start the motor.
And 2017 and 2018 priuses use a Lithium battery pack, so in that case, Mr Shouty was right!
https://www.quora.com/How-does-a-Prius-starter-work