Any other Biblical writer would not resort to circumlocutions. He would say straight out, “Relief and deliverance will come from God”. What is our author thinking of when he talks about “another quarter”? Is there some rule against God getting a mention?
One view is that since later generations would celebrate Purim with all kinds of frivolity, a direct mention of the Divine Name might have led to sacrilege. Another argument is that gentiles, reading that the Jews vanquished a non-Jewish ruler, might treat the Book with disrespect.
Whatever the situation, the fact is that the story clearly serves God’s purposes and the Divine hand is at work whether it is acknowledged or not. (One must add that when the text speaks of makom acher, “another place”, some weight must be given to the post-Biblical use of Makom or HaMakom for God in the sense of the One who is in every place.)
Not everyone realises that there is a second Biblical Book which omits the Divine Name – Shir HaShirim, the Song of Songs, where the nearest we get is Chapter 8 verse 6 where there is a word which some translate as “a flame of the Lord”, though the meaning is really no more than “a very mighty flame”. The omission of God from Shir HaShirim may be because the Book is capable of being read as a series of explicit human love poems, though the traditional view is to see it as an allegory of the love between the Almighty and Israel.