No. Facebreaker cannot be played on PlayStation 2.
Release Date: Facebreaker launched in September 2008.
PS2 Lifecycle: The PlayStation 2 was officially discontinued in January 2013, but major publisher support ended years prior. No 2008 titles were released for it.
Actual Platforms
Xbox 360
PlayStation 3
Microsoft Windows (Games for Windows Live)
If you want a boxing game on PS2, look at Fight Night Round 3 or Ready 2 Rumble: Revolution.
