I don't think that being recognized for success is a basic human (psychological) need. It certainly isn't mine. Sure, I like to be successful in what I do, but I only need internal recognition for that, i.e. people using something I built and being happy using it, not external (people actually thanking ME for having built it).
I think longing for external recognition is a sign of a deeply wounded soul, of a person lacking the most fundamental self-love and self-esteem.
I think you're correct, that internal happiness is incredibly important but being recognized by others is a basic human need. In fact, it's listed in the Esteem portion of Maslow's Hierarchy of needs. Esteem is one of the primary layers, and within it are both self-esteem and respect from external parties. It's a basic human desire to be accepted and valued by others. If you've gotten over the need to have acceptance by others, that's awesome. However, that doesn't mean it isn't a basic desire.
I think longing for external recognition is a sign of a deeply wounded soul, of a person lacking the most fundamental self-love and self-esteem.