So it turns out in 2005 there was a Czech project for Becherovka (a Czech liquor) where people created tons of flash games promoting the alcohol. There was a "sort-of" recent upload on youtube that shows a collection of these games and also includes Bechercup 2005.
https://www.youtube.com/watch?v=YurqyZ7Hcy4 (the game is mentioned at 10:12)
Still waiting for a reply from Adam, I am really hoping he created the game, however, I don't know if he's gonna remember the name of the song now.