The concept of the video was Boy George as an outsider, getting kicked out of different places in various historical settings. It was directed by Julien Temple, who came up with the idea of jurors dressed in blackface. This was a shocking image for American audiences, who long associated blackface with racism, but in England it was far more accepted as part of their music hall tradition.
Temple explained in the book I Want My MTV: "'Do You Really Want To Hurt Me?" was about being gay and being victimized for your sexuality, which George was kind of emblematic of. It seemed appropriate to me that in the video he would be judged by jurors in blackface, to send up bigotry and point out the hypocrisy of the many gay judges and politicians in the UK who'd enacted anti-gay legislation."
Rooster"s answer is more than I had heard / read around the time the song came out, but I suspect it is spot on.
I would add that I heard / read that it was occasioned by a breakup with his partner.