Petscop is an unfinished, unreleased Playstation 1 game developed in 1997 by a company called Garalina. As far as we can tell, Garalina is a fictional game development company and/or they were never known to the public due to the game never being finished.
It's disputed whether Paul plays this on a PS1 or an emulator on his computer. Although he does seem to reference some physical copy of the game, it is technically possible to put game emulation files on a disk which can then be played on a computer.
The primary gameplay revolves around “catching” creatures referred to as “Pets”. Despite the fact that they are called “Pets”, the game use words such as “somebody” and “someone” to refer to them, both words used only to refer to humans. This could hint at a connection between Pets and humans/children. According to the sign at the start of the game, Petscop was meant to have 48 Pets in total. We know there are only 6 Pets in the first level Even Care. It seems the original game planned on containing 8 levels (or “homes”) with 6 Pets in each level.
The menu of Petscop contains the usual suspects: Resume Game, Options, Pets, Quit Game. But it also contains a curious option called “Book of Baby Names”. There is no consensus what the meaning of this option is. It’s random nature might indicate a clue regarding the names of characters in the game. It could also be a reference to adoption, where the new parents will often rename the children (such as Candace Tiara Elmore being renamed to Candace Elizabeth Newmaker). In Petscop 6, Paul shows us that “Book of Baby Names” does nothing upon selecting it. He guesses that at some point you would be able to name your Pets, and the Book of Baby Names would give you name suggestions. This further strengthens the connection between Pets and humans/children, as generally you wouldn’t name your Pet a human name (although many people do).
The meaning of the word “Petscop” is still unknown and/or under discussion. The most obvious theory would be a combination of PETS + COP, as the goal of the game is to pursue or trick pets so that you can “catch” them.
Another theory: The word “scop” has ties to meanings such as scold, scoff, abuse, derision, mock. If “Pets” are related to humans or children, this could be a further connection to the child abuse themes in the game.
It could also be a misspelled version of the word "Petshop". When Shadow Monster Man is writing his sentences in Petscop 6, he frequently misspells words. Since this would have to be programmed deliberately, Misspelling may be a theme.