When I read those first two sections I didn't like the guy either, but he arrives at some much healthier takes by the end of the piece. So I think it's intentional to illustrate his growth and the fact that he's willing to put the vulnerability and the mistakes up front and own them to me suggests that he really does get the "secrets" of being socially well adjusted.
My own view is that it's about giving generously to other people without expecting anything in return. People are surprisingly reluctant to do this, but if you do, most people will like you. What are you supposed to give? Well it can be just about anything, time, attention, compliments, money, ideas, a shoulder to cry on, you name it. But probably the most powerful thing if we're talking about building social relationships is to give them your personality. Think of it like there is a big empty jar out there which represents the social environment and we're all wired to not want it to be empty, well go and fill it up with your personality, provide examples of who you are instead of standing off in a corner silently and going unnoticed. Instead of being forgotten you'll be remembered, many will like you, some will love you and some will hate you, the ones who respond most positively are the ones you make an effort to engage with in the future.
Sasha starts figuring this out when he starts working at the fancy restaurant with waiters who would do really odd stuff and it would work. The best waiters were for the most part just displaying a lot of personality. Working at restaurants might have skewed his perspective a bit because when you work as a waiter you're putting on a performance, the goal is to do a job, entertain, get compliments and get tips, beyond the food this is why people go to a nice restaurant. Being authentic and building lasting relationships is secondary to performing a commercial service at a restaurant, but not in real life (and perhaps not at the highest levels of certain commercial services for that matter, the line starts to blur). I think he's realized all this by the end of the article.