People (judges, arbitrators) imply terms in contracts all of the time. It doesn't have to be explicitly stated.
They would try to get at the "spirit" of the clause, as best then can, by reading the entire agreement. IMO the spirit of the clause - what the parties had in mind - is that the Yankees would be benefiting from him succeeding and reaching those milestones as much as A.Rod would be. In reality that's not going to happen though.
I would like A Rod's chances in an arbitration but I think there's at least some merit to the Yankee's position.