Accoring to one website
Björn has said that ‘The Name Of The Game’ is about a woman falling in love with her psychiatrist, though not necessarily Agnetha. In the June 2005 interview on the ABBA - The Movie Limited Special Edition DVD, director Lasse Hallström says that he requested the lyric specifically for the dream sequence in the film featuring a psychiatrist and patient.
The game played in the film clip is Fia or Fia med knuff, similar to the English game Ludo.