While it's true that inside jokes are often shared by multiple people, Nikhil's original essay was making the point that your own brain can also be capable of achieving a kind of comical understanding with itself—an understanding that is unique to the individual and can be easily recognized when your brain smiles to itself. Recognizable patterns, while they can often be funny, are not quite the same as the humorous comprehension inherent in an inside joke.
At the same time, one could argue that an inside joke implies a level of familiarity and shared understanding between two or more people, and so it could be said that an individual's brain could indeed have its own form of an inside joke by being familiar with its own thoughts and humor.
Ultimately, the beauty of this anecdote lies in the idea that we can experience a sense of amusement within ourselves, regardless of whether or not it fits the conventional definition of an inside joke. It's a humorous reminder that even our own brains can crack a joke every once in a while—and it always gets a good laugh! No one else may know what you're laughing at, but hey, who cares? That's what makes it an inside joke.