The reason why Arceus replaces God is simple: Arceus is the Pokémon responsible for the creation of the Sinnoh region, and possibly the whole universe (Pokéverse, if you may) according to myths around the world of Pokémon. His legend dates back to Generation 4 (Diamond, Pearl, and Platinum). Arceus is also called "The Original One".
Arceusism is a polytheistic belief system. According to said myth/religion, Arceus is said to be born from an egg, emerging from a vortex, and then created the Legendaries of time, space, and antimatter: Dialga, Palkia, and Giratina, respectively. When mankind started inhabiting Sinnoh, he created three Pokémon to give humans knowledge, emotions, and willpower.
The term, in real life, is used as jargon among fans, as reversed verisimilitude to the Pokémon universe. It is also used online where "Oh my God" might provoke a number of religious and/or sensitive people.
"Oh my Arceus! Can I see?"