Gruß Peter!

> What it means: my guess -- a person's need for validation

Yep - I wrote pretty much the same in German (nach Anerkennung suchend) cause I thought it might be some guessing game I didn't know about and I didn't want to spoil it :-§

The term is (I assume) pretty common in psychology, e.g. with regard to a child's need for attention and self-actualisation, or whatever it's called. It is known to me, anyway.

> I would think it needs the genitive s, because the need is a property of the thing needed.

Makes sense though I've never thought about it. It just sounds right when said to me. I'd try to explain it like this though:

The genitive applies in cases like this: "lobenswert" ('commendable') means "des Lobens wert", or "wert, gelobt zu werden". "Geltungsbedürfnis" could be parsed as "Bedürfnis nach Geltung". Let it suffice to say that two substantives compounded here require this bridging 's' between them and that this is self-evident to German speakers. Maybe Herr Sieber could add something useful, I dunno.