It is δόξα τω Θεώ, with the tiny marks under the omegas, it's in dative which has been dropped and it means δόξα στο Θεό indeed. It currently means glory and the phrase is like "Praise the Lord" or used as "thank God".
I don't know when the meaning of the word shifted. There is a huge distance between the Ancient Greek used in church (think 300AD onwards) and very Ancient Greek from the classical era but it is a continuum, right? "Belief in the Lord" is basically "have faith" and I don't think that this is too far away from "praise Him" in a religious context.