He correctly starts by pointing out that how we answer the question of whether Jews and Christians worship the same God is a key clue and building block toward answering the former question regarding Muslims.
The answer to the question of whether unregenerate Jews and Christians worship the same God is answered quite clearly by Jesus when he addressed the Jewish leaders of His day:
John 8:42 Jesus said to them, “If God were your Father, you would love me, for I came from God and I am here. I came not of my own accord, but he sent me. 43 Why do you not understand what I say? It is because you cannot bear to hear my word. 44 You are of your father the devil, and your will is to do your father's desires. He was a murderer from the beginning, and has nothing to do with the truth, because there is no truth in him. When he lies, he speaks out of his own character, for he is a liar and the father of lies. 45 But because I tell the truth, you do not believe me. 46 Which one of you convicts me of sin? If I tell the truth, why do you not believe me? 47 Whoever is of God hears the words of God. The reason why you do not hear them is that you are not of God.”Of particular note: Despite being monotheists, if other worshippers of other religions do not love Jesus and acknowledge him as Lord, then they do not know God the father. In addition, if they do not listen to the word of Jesus, then their father is the devil. That's pretty blunt. Furthermore, by stating, "before Abraham was, I am", Jesus is pre-dating Isaac and Ishmael, which is significant to both Jews and Muslims.
Before Abraham Was, I Am
48 The Jews answered him, “Are we not right in saying that you are a Samaritan and have a demon?” 49 Jesus answered, “I do not have a demon, but I honor my Father, and you dishonor me. 50 Yet I do not seek my own glory; there is One who seeks it, and he is the judge. 51 Truly, truly, I say to you, if anyone keeps my word, he will never see death.” 52 The Jews said to him, “Now we know that you have a demon! Abraham died, as did the prophets, yet you say, ‘If anyone keeps my word, he will never taste death.’ 53 Are you greater than our father Abraham, who died? And the prophets died! Who do you make yourself out to be?” 54 Jesus answered, “If I glorify myself, my glory is nothing. It is my Father who glorifies me, of whom you say, ‘He is our God.’ 55 But you have not known him. I know him. If I were to say that I do not know him, I would be a liar like you, but I do know him and I keep his word. 56 Your father Abraham rejoiced that he would see my day. He saw it and was glad.” 57 So the Jews said to him, “You are not yet fifty years old, and have you seen Abraham?”  58 Jesus said to them, “Truly, truly, I say to you, before Abraham was, I am.” 59 So they picked up stones to throw at him, but Jesus hid himself and went out of the temple. (emphasis mine)
Volf also mentions that he thinks the Muslim "referent" is the same God, because they worship a sovereign creator that bares many likenesses to our Christian God. However, this description matches more closely with Chapter 1 of Paul's letter to the Romans:
"19 For what can be known about God is plain to them, because God has shown it to them. 20 For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made."
Calvin, in Book 1 of the Institutes of Christian Religion, gives a great exposition of how general revelation, while leaving all men without excuse, is also denied and corrupted by the human nature, so that rather than man worshipping God truly, according to His will as proclaimed in the Bible, mankind instead turns that worship into idolatry. This seems to explain really well that Muslims do not worship the same God, even if they start with a referent equivalent to a generic, sovereign, impersonal creator, one who is known to all people through general revelation. They may start with this common understanding, but it is more important to understand that they go further -- rejecting Christ, adding to the scripture, adding Mohammed, and worshipping a different god, named: Allah.
Volf argues incorrectly that peaceful cohabitation between Muslims and Christians depends upon admitting that both religions worship the same god. True shalom can only be experienced and known through the Gospel of Jesus Christ. Pray for both Muslims and Christians to know the only One who can bring true peace.