It means that Gogol feels free from the influence of his overbearing family and their culture from which he has always struggled to distance himself.
Gogol spends his adolescence and young adulthood trying to escape from the influence of his Bengali parents. He hates the strange name they've saddled him with, so he changed it; he struggles with the tension between his own family's customs and his preferred American ones. Maxine and her parents are complete opposites from Gogol and his own parents, which explains why he enjoys their company so much--where his own mom and dad are cautious about everything and keep their own romance private, for example, Maxine's parents live a carefree, openly affectionate lifestyle. And while Gogol is expected to show respect and devotion to his parents, Maxine enjoys spending time with hers, as if they are her friends, her equals.
While living at Maxine's family home in New York, Gogol feels happy, but there's always a chance that his mom or dad will call him there on the phone and embarrass him. At Maxine's vacation home in the wilderness, though, Gogol feels "utterly disconnected from the world" and likes it. There's a phone in the main house that rarely rings, the narrator tells us, and no phone at all in the small outbuilding in which Gogol and Maxine sleep. In fact, Gogol's parents don't even have the phone number for the main house. And the number isn't listed in telephone directories, either. It's a truly private place where Gogol is comfortably ensconced and completely unreachable by his family and the suffocating obligations they typically impose on him. This is why he feels free at the end of Chapter 6, sleeping peacefully there with Maxine.
Is he really free? Probably not. The vacation is temporary, so pretty soon he'll be back in New York, a phone call away from his parents. In fact, soon after this night, Gogol will lose his father forever, and while he's grieving, he'll also lose the connection he'd had with Maxine--they will break up, eradicating the whole carefree, indulgent lifestyle he'd enjoyed with her family. So, no, the freedom Gogol feels in the cabin that night with Maxine is neither real nor permanent. Taking a wider perspective, Gogol is also still trapped in his youthful failure to understand his own parents, their culture, and especially his father's deep connection with the author Gogol.