In sports, being a team player would mean something like you don’t play football as if its all a one man show. But at work isn’t this kind of independence a desirable thing? Like salespeople who have to carry their own weight at all times? At this point, looking at all these job ads is giving me the impression that what it really means is “submissive and obedient”.
It’s just a cliché, don’t worry about it. They have to write something, and as it’s hard to write a good job description, they write stupid things like this.