Yes, the original Gameboy game was first. The other branches followed quite quickly though, so they probably fed into each others popularity and I'm not sure it would have made a huge difference if e.g. the anime had come first and a bit later then the games. EDIT: that all these channels were there was probably quite important though.

Japanese releases:

Game: early 1996, second late 1996

TCG: late 1996

TV series: 1997

movies: 1998