Rocky wasn't a washed up boxer. The character was written as a talented amateur boxer that successfully proved himself against a top professional boxer.
In a way, the 2006 film Invincible, being the story of Vince Papale, has the same plot. Both films are also set in 1970's Philadelphia.
You might want to re-watch Rocky. It opens with him taking a terrible beating in a backroom ring. At the start of that film he's down on his luck, living in the ghetto, and breaking legs for a hood to make rent. He's punch drunk. His prospects are so bad Mick turns him down when Rocky asks to train there. Then the miracle chance gets thrown his way and Mick changes his mind.... If it wasn't for that miracle chance his career was over.... Rocky was the story of a man so far down he can't SEE up and he overcomes that extreme adversity to draw the Champion.
"Chariots of Fire isn't a biopic, it is a story about preparing for the Olympics. What made that story compelling wasn't the sport, but the competing interests of church, state, social class, family, and glory. Get all of those elements together in a chess movie, and you may have a hit."
And there's no reason you couldn't get most if not all of those elements in a chess movie.
Bronstein was 17 when the Nazi's invaded. His eyesight was too poor to be a soldier so they had him play chess with wounded men in hospital. A great screenwriter could turn that story into an excellent script. Get the right Director and casting and you've go something.
The story of his match with Botvinnik and all the politics surrounding that contest could also make an interesting subject.
Morphy's tragic final days should make a dramatic work if the screenplay is right.