Never put too much faith in google translator :) In a chess-related context, busted is certainly not translated as "rotto" (which equates to "broken").
I'm not sure about an exact equivalent of busted. In my mind i translate it as "spacciato", as in "il nero è spacciato" ("black is busted"). Spacciato more or less means "hopeless".
Hmmm, Guioco Rotto, I've had a few of those