Ugh, yeah, I did know that. A Westminister system is not really a republican form of government in the sense that the legislature elects a Prime Minister from its ranks (though that is not always the case, like in France, for example).
Now while it may be inconceivable to you that a republic could exist that would not have a system of divided powers, that is not part of its definition. Indeed, it would be in theory possible to have a republic in which one elected body, or even a single elected person would have the legislative, judicial, and executive powers combined.
At the time the Constitution was adopted, and for a number of years afterward, there were states that had the legislature elect the governor and there were some in which the legislature also had judicial powers beyond those of mere impeachment.
