When comparing two people or things, the correct degree of comparison is the comparative form — not the superlative.
"Better" is the comparative form of "good", while "best" is the superlative used for comparisons involving more than two.
Therefore, "the better of the two" is the grammatically correct construction.
(A) "the best of the two" – Incorrect; superlative used instead of comparative.
(B) "the better of the two" – Correct comparative form.
(C) "the good player of the two" – Incorrect adjective choice.
(D) "the best player of the two" – Again, incorrect use of superlative.