I think it is always important to understand context and perspective.
While philosophically speaking, The Muslim God is the same one as the Christian God, this is not true from every perspective.
Simply from a Theological perspective:-
Allah is a God that wants Pagan’s murdered or enslaved. The Christian God wants us to love everyone. NOT THE SAME GOD.
Allah revealed the Koran and it therefore contains Divine Revelation. The Christian God has not made public revelation other-than what is in Scripture
I could go on and on, but I am sure you understand what I am getting at.
So I think it is important to understand WHAT perspective the CCC speaks on when it speaks about Muslims having the same God. I believe the Quote in the CCC is from the Lumen Gentium (could be wrong) which specifically speaks of how close other faiths are to the truth. In that sense, yes Muslims have it right in that they believe in a Mono-Theistic God with most of the philosophical properties we give to God. But if we try to carry this over to all perspectives, we create a lot of confusion and perhaps even incorrect conclusions.