Although Greeks and Italians may make a lot of their differences, they are essentially the same, differing from the Egyptians, Babylonians, Persions and other middle-eastern rulers. So, the Greek empire, the Roman empire, the Holy Roman empire and WesternCivilization are what is being referenced in the term `their kingdom`.
The transgressors coming to the full speaks to 2The 2:1-8 where it is called rebellion and wickedness.
The great rebel, beast, antichrist will be an intellectually, econominally and politically gifted person.