I believe that each player controls 1 mech. But you draft 4 cards. So in a 2 player game, each mech will get 2 cards, in a 3 player game 2 mechs get 1 card and 1 mech gets 2 cards, and in a 4 player game each mech gets 1 card.
This is correct. It's a very small section in the tutorial booklet that states that you always draft 4 cards, so in a two-player game each player drafts two cards each round