The footage from this movie was taken from Yu-Gi-Oh! the Movie, a movie which debuted in Japan on March 6, 1999. The reason the animation looks different in this movie compared to Yu-Gi-Oh! Duel Monsters was because this movie was produced by Toei Animation, the same animation studio that produced the first Yu-Gi-Oh! animated series (erroneously referred to in some communities as "Season Zero"). As with the Toei series, this movie was never officially released in the United States.
The part where Yugi says that he and Joey live in Japan is a reference to the fact that in the English dub of Yu-Gi-Oh! Duel Monsters, the series was Americanized to where Domino is located somewhere in the United States. "Egyptian Exhibition Expo 2007" pokes fun at this fact as well.
The reason Kemo's hair looks different in this movie is because he was drawn based on his appearance during the Death-T story arc in the manga. His hair receives its familiar look during the Duelist Kingdom story arc in the manga and Yu-Gi-Oh! Duel Monsters.
When Yugi asked Kemo if he's supposed to be working for Pegasus, it's a reference to the fact that it's revealed in the manga and a Japanese episode of Yu-Gi-Oh! Duel Monsters that Kemo is actually a spy sent by Industrial Illusions to work for Kaiba Corporation. The English dub of Yu-Gi-Oh! Duel Monsters ignores this fact completely.
Gary's lines "I musn't run away! I musn't run away! I musn't run away!" are Neon Genesis Evangelion references which were Shinji Ikari's lines.
Gary Stu is, in fanfiction, the male counterpart of the Mary Sue, since Shougo feels much like a self-insert character for the audience to project themselves into.
The caption at the end of the credits explaining that Gary was sent to an island to kill off his classmates one by one is a reference to the Japanese movie Battle Royale, where students from a selected class were forced to kill each other on an island due to a law passed by the government to deter the country's youth from rebelling against the adults.