I don’t know about anime series, but the novel “Ready Player One” by Ernest Cline is a lot like this. The MMO (massive multiplayer online [game] for those who have no idea what this question is about) is so popular that most of humanity spend their everyday lives in it. It’s equal parts Second Life, World of Warcraft, and The Matrix. People shop and go to school, level up characters, go on quests and adventures, get armor, spaceships, etc. The whole book is a loving homage to 80s nerd culture, and the “quest” in the novel is a video game easter egg hunt.