I was reading a film review and came across a phrase "Michael, played by the very game David Kelly". I guess "game" must be an adjective, meaning something like "energetic". Am I right?

PS the dictionary does have some definitions for the adjective "game" but they don't seem to go with the word "actor":
willing to face danger; frivolous; full of fighting spirit; prepared or willing, etc
The synonyms you list seem appropriate to me (except "frivolous"). I would say "up to the challenge - willing to respond immeditately to the challenge, doing whatever is required." Many acting assignments require such a person. And some actors even do their own stunts.
Your explanation is very clear, thank you! Emotion: smile