Not only is he using the name, setting and the characters, visually it's imperceptible from the TV-series. It's so good that you could probably send screenshots of it to Kotaku and they'd think it's the official Family Guy game which means it has the potential to cause tangible damage to the image of the series and just the possibility of that will come with lawyery hellfire unseen by any coomer ever before.Have you not heard of any of the shit Nintendo does?
They go after literally anything using their IP, including porn games. You're lucky if you only get off with a C&D. If anyone tries to pull the fair use card, or tries to fight back in any way, they'll take you to court, and they WILL win, no matter what.
Even if you have a solid argument, they'll appeal and appeal to keep the legal battle going as long as possible until you're financially incapable of fighting anymore, so you'd have no choice but to settle things in their favor. If the judge actually does rule in their favor, they'll make an example out of you by suing your entire bloodline into destitution for however long it exists.
Any big company can do this, especially Fox. They have more funds and lawyers than any average joe could ever hope to have, and they WILL bring them out if you try to defy them.
The fact that this guy is not only using the characters and setting, but is straight up using the actual name of the series in the title of the game puts them right in Fox's crosshairs. If they come knocking, you should just cut your losses and move on.
Only thing that could save the dev from being doomed to an oubliette is if he renames the game, swaps the family being followed to some other before unseen family (like a spinoff) and prays to all the deities every night.