Sigma appeared at the doorway with the intention of blocking him in, uncertain Wyatt would listen otherwise, and holds firm in spite of the warning. The mentor had not made mention of Sigma's past as a Gamemaker after he'd revealed it, and the Doctor assumed he was being avoided. Based on their rocky history, he found it doubtful that Wyatt would play nice. But if he did not, Sigma's would make himself one of the Rebellion's targets before he even had a chance to share what he had learned...

He uses his first name to remind him that they once shared drinks, before the Games made him bitter with loss. "Wyatt, it is Sigma. I am not here to stop you, but you must listen to me once more." It's not a request. "My life depends on it. You're the only one I can trust."

It's a lot to wager between men who had once been enemies.