The only card he appears to draw is Palladium Oracle Mahad. As this portion of the duel is not narrated, nor is the 'card's' effects described in any way, there is no guarantee the in-movie card matches its real-life counterpart exactly, but the real card's effects suggest they are played similarly.
Picture taken from Deviant art
Updated answer based on wikia summary
It's all explained in this wiki, see the summary section on that link.
Below is the recap when Yugi fainted on turn 4, until he summoned Mahaad.
face-down "Metalhold the Moving Blockade", letting him target any
number of Level 4 Machine-Type monsters he controls and Special Summon
"Metalhold" as a monster (0/0) in Attack Position, then equip those
monsters to it to increase its ATK by the combined ATK of the equipped
monsters. "Silver Gadget" and "Gold Gadget" are equipped to
"Metalhold" (0 → 3200).
"Metalhold" prevents other monsters from being
targeted for attacks, so the attack is redirected to "Metalhold". As a
monster he controls would be destroyed by battle, Aigami activates his
face-down "Cubic Defense", preventing its destruction and letting him
Special Summon two monsters from his hand with the same name.
He Special Summons two more "Crimson Novas" (3000/0) in Attack Position.
The second "Crimson Nova" attacks and destroys "Pandemic Dragon"
(Kaiba: 4500 → 2000). As it was destroyed, the effect of "Pandemic
Dragon" activates, reducing the ATK of all monsters on the field by
1000, but the "Crimson Novas" are unaffected as "Pandemic Dragon" had
less than 3000 ATK ("Metalhold": 3200 → 2200). The third "Crimson
Nova" attacks and destroys "Metalhold" (Yugi: 5000 → 2800).
As two of his "Crimson Novas" destroyed monsters by battle this turn,
they may both attack again via their effects. They attack directly,
but Yugi activates his face-down Continuous Trap Card "Spiritual
Swords of Revealing Light", letting him pay 1000 LP to negate an
attack. He pays 2000 to negate both attacks (Yugi: 2800 → 800).
Aigami activates his face-down "Unification of the Cubic Lords", letting him
Fusion Summon a "Cubic" Fusion Monster using monsters from his hand
and field as Materials. He fuses his three "Crimson Novas" to Fusion
Summon "Crimson Nova Trinity the Dark Cubic Lord" (4500/3000) in
Attack Position. "Crimson Nova Trinity" attacks Yugi directly, with
its effect activating as it attacked, halving his opponent's LP (Yugi:
800 → 400; Kaiba: 2000 → 1000). As an opponent's monster declared a
direct attack with a monster whose ATK is greater than or equal to his
LP, Kaiba activates his face-down "Krystal Avatar", Special Summoning
it as a monster with ATK equal to his LP (1000/0), then changing the
attack target to it. "Krystal Avatar" is destroyed (Kaiba: 1000 → 0).
The effect of "Krystal Avatar" activates as it was destroyed by
battle, inflicting its ATK as damage to the opponent. (Aigami: 5000 →
4000). Aigami activates the effect of "Crimson Nova Trinity" to
inflict damage to Yugi equal to the damage he took, but Yugi activates
the effect of "Clear Kuriboh", sending it from his hand to the
Graveyard to reduce the damage to 0. Since it destroyed a monster by
battle this turn, the effect of "Crimson Nova Trinity" lets it attack
again. "Crimson Nova Trinity" attacks directly, with its effect
activating, halving Yugi's LP (Yugi: 400 → 200). The attack continues,
but Yugi activates the effect of the "Clear Kuriboh" in his Graveyard
as an opponent's monster is attacking directly, banishing it from his
Graveyard to draw a card. If it is a monster, he can Special Summon
it, then the opponent's monster will be forced to attack it.
At this point, Yugi cannot continue, but Atem returns to the world and takes over.
Atem draws "Palladium Oracle Mahad", then Special Summons it (2500/2100) in Attack Position via the effect of "Clear Kuriboh",
redirecting the attack to it. "Crimson Nova Trinity" attacks "Mahad",
with the effect of "Mahad" activating as it battling a DARK monster,
doubling its ATK (2500 → 5000). "Crimson Nova Trinity" is destroyed
(Aigami: 4000 → 0).