The phrase 'kingdom of God', therefore, which occurs only sporadically in texts of this period, functions, when it occurs, as a crucial shorthand expression for a concept which could be spoken of in a variety of other ways, such as the impossibility of having rulers other than Israel's god, or the divine necessity of reversing the present political situation and re-establishing Israel, Temple, Land and Torah. This complex concept picks up and join together the whole social, political, cultural and economic aspiration of the Jews of this period, and invests it with the religious and theological dimension which, of course, it always possessed in mainline Jewish thinking. (p303)
To speak of the kingdom of this god does not, therefore, mean that one is slipping into a dualistic mode of thought, or imagining that the event which is to come would be related only marginally to space-time events. This kingdom was not a timeless truth, nor an abstract ethical ideal, nor the coming end of the space time universe. (p307)
from NT Wright, NTPG
The texts in question are those of 2nd Temple Judaism, but if we accept Wright's analysis of them then this should also factor in our interpretation of the NT use of the same phrase. The question is not whether or not Jesus re-interpreted the phrase when he used it, he did, but how did he do so and what areas of conceptual and aspirational overlap remained?