This is the 2540th most frequent Russian word.
российскому
"Российскому" means "to the Russian" or "relating to Russia" (adjective, dative case).
The word "российскому" is in the dative case, indicating the indirect object (to whom the letter is addressed).
Я пишу письмо российскому президенту.
I am writing a letter to the Russian president.
"российскому" is in the dative case here showing possession, as the prize is related to the athlete.
Этот приз принадлежит российскому спортсмену.
This prize belongs to the Russian athlete.
Here, "российскому" modifies "закону" in the dative case, demonstrating conformity or adherence.