Yugi transforming into Knuckles the Echidna instead of Yami refers to "YouTube Poop: The Most Epic Card Game Ever" (which has been taken down, apparently).
Téa breaking the screen of the Nintendo 3DS by pointing at it is another reference to "YouTube Poop: The Most Epic Card Game Ever", in which Téa fires a laser from her finger at Kaiba, who deflects it with a card.
Kiba's Angrish reaction to Tea breaking the screen to his 3DS uses a clip from Deepercutt's Spiderman movie poop Revenge Of The Madman.
Catch-Phrase: Kaiba's SOLITAIRE. He uses it in intro sequences, to intimidate his opponents, brag about himself and to even answer phone calls.
Fate Worse Than Death: The poop ends with the heroes stuck in limbo, forced to listen to Pegasus singing for the rest of eternity.
Jerk Ass: Yugi. He taunts Joey about having better cards (and better Game Boy games) constantly, steals Joey's deck, refuses to duel Kaiba after his grampa begs him to after being beaten by Kaiba, and only duels Kaiba to get his GameBoy back. Téa says it best: "Joey's just starting to get the hang of the game, but Yugi's an asshole!"
Kaiba, too. He was willing to sell his little brother just to get the card he wanted.
Also, Yugi's grampa. When Yugi first asks to see the rare card, Grampa just gives him the middle finger in response. Later, during his duel with Kaiba, Yami pulls out a card of... Grampa giving the finger. Yami's remark sums it up perfectly: "My grampa is a douche!"
Out with a Bang: Kaiba apparently orgasms after being obliterated by Yami's Mind Crush.
Screw This, I'm Outta Here!: Not in the poop itself, but Deepercutt mentions in the description that he made it shortly after walking out of his 20th birthday party.
The whole poop revolves around Kaiba trying to obtain the Blue-Eyes White Cena card.
When Yami and Kaiba first start to duel, a clash from Yu-Gi-Oh! Dark Duel Stories is shown.
Sonic the Hedgehog (2006) is shown in the intro as the "power" that the Pharaoh sealed away. Later, the narrator talks about Yugi unlocking the secret of the Millennium Falcon and being destined to save the world from Yu-Gi-Oh! games, as Yu-Gi-Oh! Dungeon Dice Monsters, Yu-Gi-Oh! GX: Tag Force Evolution and Yu-Gi-Oh! 5D's: Wheelie Breakers go by on screen.
When Kaiba reveals his reward, a 3DS, Yugi's grandpa says, "My precious!".