Seto's presence as Christian Rosenkreuz is one giant heap of Fridge Brilliance. The origins of the "real-life" Rosenkreuz are Shrouded in Myth (if he existed at all is debated), but the manifestos documenting his life put his date of birth in 1378, while the war of the Roses took place in the mid to late 1400s. Furthermore, Rosenkreuz had nothing to do with Richard III or the War of the Roses. So why is Seto cast as Rosenkreuz in the role of Richard III's enforcer?
Rosenkreuz founded a secret society called the Order of the Rose Cross, which studied ancient knowledge he purportedly learned on pilgrimages in the Middle East, and their sigil was a cross with a white rose in the middle. This symbolically connects Seto to the Yorkists via their own white rose sigil, and perfectly ties into Seto's goal to summon an ancient Card God from Egypt. Rosenkreuz was said to have lived to be 106, and since magic is well known to exist in the Yu-Gi-Oh! universe, it's totally plausible Rosenkreuz was able to retain his youth for his century-long life. Finally, Rosenkreuz's date of death is 1484, and the Battle of Bosworth field which is the climax of the game took place in 1485. Thus one only needs to fudge the dates just a little bit to make all this work, because after the battle with the Card God at Stonehenge, which happens very shortly after the Battle of Bosworth Field, Seto and the Rose Crusaders vanish from England and are never seen again.
In short, someone on the development staff clearly put a lot of thought into working the legendary Rosenkreuz into the plot in a way that makes total sense internally.
Seto was preparing to fight Yugi before the Rose Duelist showed up, either by challenging Yugi in Brest or waiting for Yugi to invade England. This can be seen in his deck, where he "main-decked" many cards to counter Yugi's strategies. His Royal Decree negates Yugi's Mirror Force and Negate Attack. His Anti-Raigeki negates Yugi's Raigeki. His Magic Jammer negates Yugi's Swords of Revealing Light and ritual spells. Even his preferred battlefield, Stonehenge, is full of Sogen terrain, which disadvantages Yugi's many spellcasters. His Deck Capacity is only slightly lower than Yugi's, so he could feasibly challenge Yugi any time he needed to.
Bakura is on Yugi's side as Jack Cade, who in real life was executed for leading a rebellion against Henry VI, Yugi's father. While this fits with Yami Bakura/Thief King Bakura's character, who rebelled against the Pharaoh because of his father, why Yugi trusts him enough to make him second-in command is a mystery. Yugi is also more villainous than most portrayals, which brings up the possibility of Bakura influencing him. (Though, this last part only applies if the player sides with Yugi. If the player sides with Kaiba, Yugi's a Graceful Loser who nevertheless vows to win the war.)
