Allah is the Arabic word for God. There is only one God, the creator of us all. I agree that these Islamists do not worship God, but most Muslims do.
If we are to defeat this enemy, we must be able to identify them. This "kill them all and let God sort them out" stuff is not the answer. Were we to do that, we would never be able to stand in His presence, and that would surely be worse than death.
I am not a turn the other cheek type person, much as I have tried, it's quite beyond me.
Remember, there was a day when Christians hated and persecuted Jews, and there was a day when Protestants and Catholics killed each other, but we have grown beyond that.
Do we have to defeat this thing? You bet your life we do. Do we have to exterminate the vermin who perpetrate it? Yep and we're going to do exactly that. Do we have to sacrifice our souls to save our bodies? Nope, not if we keep our heads. Nothing, I repeat NOTHING is worth disappointing God and that's exactly what we would be doing if we wipe out a bunch of innocent people deliberately.
That is where the error is.
I don't know if you are Christian or Jewish (I am both)...but having read the Quran, I can safely say it is a perversion of the Judeo/Christian Word. It is not the fault of Muslims...they have been sold a bill of good...spoilt goods. It isn't Muslims...it is Islam.
God bless.
DS