Donkey Kong

[Mega 2]

This site says that the original "Donkey Kong" is 2-player.  How is this possible?  Who was the second player?  Luigi didn't exist yet.  The one in "Donkey Kong 64" is 1-player.

[TRM04]

Mario and Mario.  The game just takes turns alternating between one game and another.  Like if I was playing with my brother, it would be my turn     then his then my and so on but the player is always Mario.