(from the video)

It looked like they found an exploit via whatever app renders the userguide.html

Curious if they used a proxy to instead load a "malicious" page resulting in a buffer-overflow.

They using normal webkit exploit there. Reason why they start it via "userguide.html" it's because in any other case browser on PS4 can only be used when you logged in on PSN.

Of course PSN require latest firmware to work while they using device with Firmware 1.76. It's one of Sony measures to force people update firmware.

Probably a webkit exploit. The Wii U was hacked in a similar way.

Oh, same attack vector as for hacking Nintendo 3DS.

webkit, and yes, probably