Armstrong is not presenting a case for God in the sense most people in our idolatrous world would think of it. The ordinary man or woman in the pew or on the prayer mat probably thinks of God as a kind of large version of themselves with mysterious powers and a rather nasty temper.
I wouldn't be so fast to presume as to what the ordinary man or woman in the pew thinks. "A musicologist," Sir Thomas Beecham said, "is a man who can read music but can't hear it." The same is true of the person for whom religion is a strictly intellectual enterprise. Armstrong goes too far, it would seem to me, asserting in effect that the apophatic cancel out the kataphatic. It is true that an exclusive focus on the latter can be profoundly misleading, but someone firmly grounded in the former can make skillful use of the latter. Blackburn's is a very good review, though, which perhaps Gordon McCabe - who comments on a review of Armstrong's book here (hat tip, Dave Lull). "The Tao that can be named is not the Tao." What is so difficult about the notion that there is at the very center of being an unfathomable mystery?