Thanks.
I agree with your use of "partiality" as far as you go with it here. But, no, this doesn't seem to me to be his use of God's non-partiality in his argument. He takes it for a blanket statement that God treats everyone the same.
It is silly, though. Calvinism simply doesn't use the terms he uses the same way he uses them. The terms, 'Partiality', 'Love', 'Justice' and 'Freedom' all mean something different to Calvinism than what he uses them to say, and, in spite of his present use of 'Sovereignty', I can pretty well guarantee by what he has said so far, that he doesn't mean the same thing by it either, that Calvinism does.
I think he means to conclude, that if Calvinism used the terms the way he thinks they should be used, that it would logically lead to Universalism.