Yes, EarthBound exists. Known as Mother 2: Gīgu no Gyakushū in Japan, it is a role-playing game (RPG) developed by Ape Inc. and HAL Laboratory, published by Nintendo for the Super Nintendo Entertainment System (SNES) in 1994 (JP) / 1995 (NA).
It is frequently cited in "Greatest Games of All Time" lists for its writing, tone, and emotional resonance.