Should I create a extra relation-table when I have two columns in one table referencing to one column in another table
I'd definitely choose option 2. A game of chess is between exactly two players.

Option 1 allows a game with 0, 1, 2, 3 or more players, while the data model in option 2 (assuming not null on the two player columns) means that you will never have these data inconsistencies. Just remember to also add the check constraint black_player != white_player.