I took a quick look at the video. Quick info—you can deal damage to creatures and players. Creatures die if they take enough damage in a turn, and the damage resets each turn. Players die if they take 20 damage total over the course of the game.
Craig is “chump blocking”—he’s getting attacked by strong creatures, and uses weak creatures to block them. The weak creatures (the “chumps”) die, and the strong creatures remain. This leaves him extremely vulnerable, but alive. The strong creatures can attack again next turn, and he will be even less able to block them because the creatures he used to block are now dead.
He has a spell called “Char” which deals 4 damage to a target creature or player and 2 damage to himself. This could be used to destroy the attacking creature, but destroying the creature won’t win him the game. At that moment, he is at 3 life, his opponent is at 7. After chump blocking, the opponent will be able to attack and win the game next turn.
Craig decides to Char the player, rather than targeting any creature. This brings his life total to 1 and the opponent to 3. It's then Craig’s turn (because he played Char at the end of his opponent’s turn). At the beginning of his turn he gets to draw a card. He draws a card that can deal 3 points of damage. (That card is Lightning Helix.)
It was exciting because it was a gamble. He could only win if the right card was on top of his deck, and therefore, it was the right move to play assuming that he had the right card. There’s a maximum of 4 copies of any card (except basic lands) in your deck, which must be at least 60 cards. By that math, you get 1:15 odds of drawing the right card here (undoubtedly the odds were not exactly 1:15 but some other number, based on however many cards were left in the deck and however many Lightning Helix were left). The commentary on the game was that this was the “only correct play”.
Edit: And he won $31,000. Second place was $16,000.