Many people argue the Urim and Thummim was used for Divination of the Will of God, too. God spoke through Prophets as well, but mediums or the Witch of Endor are anathema.
The Bible condemns Divination in Leviticus, but there is perhaps a fine gradation here in how God chooses to communicate. Laban had Teraphim too, though we are against idols, so hardly a paragon of the Faith - though prior to the Law as noted above.
Regardless, the phrase 'have divined' need not mean that he did some sort of spell - it can easily just mean, I have 'foreseen' or 'surmised that', the former in English also potentially implying that you saw with the 'third eye' or whatever, but seldom if ever meant in that manner. It may just be poetic and respectful way of address.
