It's been translated as "Concentration Duel." It's quite simple, as the anime says. Basically, you get to summon one Monster, activate one Spell, and activate one Trap per turn. But, your deck is all spread out in front of you face-down, and all of your cards also count as being Set on the field, so I assume that a Heavy Storm could turn the game into an all-Monster duel.
They don't really explain it that well, so it would be hard to replicate. For instance, we don't know whether or not you can discard cards from your hand, for Divine Wrath for instance. Moreover, draw/search cards are completely useless, since your deck is also all of your Set cards.
So, to recreate these types of duels with real cards, some issues would have to be sorted out. Cards like Heavy Storm might have to be banned; cards that return other cards to the hand could be considered as flipping those cards back face-down; discarding could be from the deck/field/table (they're all the same) to the Graveyard, but in that case, only Set cards would be able to be sent, since face-up cards would be on the field in normal dueling.
One thing that the anime already dealt with was the usage of Traps on the opponent's turn. Since Yusei was planning to use the Scrap-Iron Scarecrow he revealed earlier to block an opponent's attack, we can be certain that Traps can be activated on the opponent's turn, though there might be a limit of one Trap per turn.
It's an interesting idea, and it might be fun to play out in real life...