@ Rattigan350: Your view about the kingdom referring to Christ & his rulership as opposed to a domain, is correct.
From Strong's & Vine's:
Βασιλεία (basileia) Royal power, kingship, dominion, rule, not to be confused with an actual kingdom, but rather, the right or authority to rule over a kingdom, of the royal power of Jesus as the triumphant Messiah, used in the N.T. to refer to the reign of the Messiah.
In Rev 1:6; 5:10, the most authentic mss. have the word basileia, "kingdom," instead of the plural of basileus, AV, "kings," RV, "a kingdom (to be priests)," and "a kingdom” (and priests).
Compare the latter reference with the NWT interpretation of Revelation 5:10. (kings!)