Ese jugador no le llega a los grandes del fútbol mundial.

English Translation

That player doesn’t measure up to the greats of world football.

This is from Spanish Idioms. If “le” refers to “los grandes”, I suppose it should be “les”.

I think the phrase is correct, although it is not usually said that way. Le refers to the player.
For me it would be better:

Ese jugador no está a la altura de los grandes/mejores del fútbol mundial.

Hope it helps.

Is that even grammatical, with “ese jugador” being the subject?

I agree. That was my first guess before seeing the possible answers.