Good question and your assumptions are right. The God they are supposed to worship is the creator of all. However, salvation can be found only Jesus Christ. This is were Islam goes its own way (as bibliographically told as "appearing as an angel of light"), and spreads "false teaching", claiming Jesus Christ as a prophet, but not a son of God. The Islam belongs to the category of people who do believe in God, but live by laws not by grace. Even in "Christianity" you will see people 'serving' Jesus Christ and be an abomination to the Lords his teachings.
My advice here is not to look to much into other "religions", let our Lord judge the followers of those. Remember what Jesus said, you will recognize a tree by its fruits. Instead of bashing the tree, just look at the fruits. Spread the Word, testify what Jesus has done for you, but do all in love.
Al-lah Al-ab as the specified muslim deity means "God, the father" and "God the Almighty One". You confuse Pagans with Muslims. Does not scripture tell you to "test everything" (feel free to test this) ?
The matters of "jihad" and terrorism and they are wrong and we are right, those conversations are childish. Rather than seeing a problem, you should see a mission there. Did you know it is forbidden to spread the Gospel in Saudi Arabia?