This is one of those "yes" and "no" questions.
Yes, in the sense that God sent the Prophet Muhammad as the final prophet for all people, and the Qur'an as revelation for all people. So it is intended for all people, and all people should do what God wills, since God is the one who created us and the universe.
However, perhaps there was some divine wisdom in creating the world in such a manner that there is diversity in faith. That is, obviously, God knew when sending the Prophet (S) that not every person in the world is going to accept Islam as a faith, for whatever reason (especially human reasons like geography, culture, language, fear of what is different, etc). This is similar to how Adam and Eve shouldn't have eaten from the tree, but at the same time Allah knew that they would eat from the tree, and doing so was part of the divine plan for humanity.
Qur'an 9:33 indicates that Islam will eventually predominate, and this is expected to happen during the time of the Mahdi. However, even the, there are some hints that some people will still formally follow other religions, even though the Mahdi will settle in as a just and welcomed ruler and will have proof of the religion with him.