Dice Ibegon's text:
"Interrupt: When you would declare an engagement, target an eligible enemy objective instead. Your opponent must declare defending units first, if desired. You must then declare at least 1 attacking unit, if able. Engage the targeted objective. (Limit once per turn.)"
The rulebook states that you can only declare an engagement against a given objective once per turn. Dice's text just "targets" an enemy objective, then "engages" it. You technically do not "declare" against the objective, as the triggered ability interrupts via "when you would declare an engagement".
Thus, the correct interpretation of this ability seems to be that Dice's ability does not count as a declared engagement, and thus you could use it to attack the same objective twice in a turn.
Can our resident rules gurus confirm or clarify?