The show is The Adventures of Puss in Boots, a spinoff of the Shrek movies. Puss in Book is just the title of the interactive one.
They’ve also done it for Buddy Thunderstruck, and Stretch Armstrong. The Black Mirror one will be the first for an adult-aimed title.
I’ve played the Puss in Boots and the Buddy Thunderstruck, and the system is pretty simple - every so often in the story (about every 2-3 minutes, IIRC), you’re given a choice between two options. Timed - if the timer runs out, it’ll just go with wherever the cursor is. Whether the decision changes the story significantly or is just a brief diversion changes from decision-point to decision point. I don’t know if the Black Mirror version will retain the ‘characters discussing the choices’ aspect that PiB and BT had, since it’s not as comedic. Since you don’t need to go flipping through pages, it’s really more of a visual novel than a game book, but that’s honestly a fine distinction.