Pronouns 'His' or 'her' are identity of a player, who takes part in the game. You can, also, use a pronoun 'their' as in the sentence: 'Target players put their top card of their library into their graveyard.' But, in this case, there is no strict identity at all.
I think they are using 'his or her', both times, for absolute clarity of instructions. If we say: "Target player puts the top card of their library into their graveyard."
The first 'their' would refer to 'target player'; but is the second 'their' referring to someone else's graveyard pile (a 'someone' referred to in a previous sentence), or some collective 'graveyard' pile of cards, that is, those discarded by all the players of the game into one pile?
To say, "Target player puts the top card of their library into his or her graveyard." is just getting too damn complicated.