I'm not sure the meaning of the following sentence.
He has worked in a game of "who's who" with specialists in his field.
what do you mean by "to work in a game of 'who's who'"?
I can't say for sure without more context, but:
A "Who's Who" is a book that lists prominent or important people, typically with a brief biography. There are many such books published by a variety of publishers.
From this, the term "Who's Who" has come to mean a group of important people. Like someone will say, "The attendees at the party were practically a Who's Who of powerful politicians".
I'm not sure what someone would mean by "a game of Who's Who". It sounds like he means that people are competing in some way. Perhaps competing to see who knows or has worked with the most important people? Or perhaps the point isn't the "game" part, but simply that this person has worked with many important specialists in the field.