I didn't either. I think he had no intention, at least not consciously, of using Vincent. And feel his decision to return to play came about in a genuine way.

I never thought Eddie had ulterior motives for stakehorsing Vincent.

Report back when you've actually watched the film.

Did Eddie even play Vincent in the tournament? I remember Eddie quit during a game with another unnamed player
Well either way one of Scorsese's worst.

What's the key lesson Felson tries to get Vincent to learn?
That winning isn't in the stickit's in the head.
Felson uses Vincent purely as a pigeon, to check out the potential competition before making a comeback WITHOUT arousing anyone's suspicion.
Frontmen are considered scum (don't forget what a lowlife George C. Scott was in "The Hustler").
So no one would suspect Eddie would ever make any kind of comeback.
But if anyone did, then they might come 'round tryin to play a psych job on him, because Eddie does house some self-doubtwhich is his only weaknessabout his remaining ability.
I think Eddie figures that Vincent is too much of a flake to ever really figure it it out.
As for why Eddie forfeited the tournament
Vincent let himself lose to Eddie on purpose during the tournament,and when Eddie found out, he didn't want to win that way to Vincent, so he forfeited. That's why Eddie told Vincent in the end, I want your best game.