On the surface, Gone Home doesn't seem to have much to do with BioShock. However, The Fullbright Company's Steve Gaynor revealed that a very tiny easter egg suggests that it is set in the same universe as Irrational's beloved Bioshock franchise--"in a totally non-litigious way," of course.
The nod takes the form of, funnily enough, a video game. BioShock 2's Minerva's Den DLC adventure was Gaynor also worked on, features an old video game titled "Spitfire". In Gone Home, a Super Nintendo game called "Super Spitfire" can be found while exploring the house.