Now aside from not actually needing to meet both criteria to be an organisation (which would make Islam one by your own admission), to state that religions are not organised for a particular purpose is odd in the extreme.
It's not two criterias for the same thing, they are two different words. By matching the criterias for a certain meaning A you don't automatically match the criterias for the other meaning B. The archer's bow is not the front of a ship.
There is organization as in:
1. Structured content (like a CD collection)
2. A structure of people working together towards a common goal (like Amnesty International)
Islam (and other religions) meets the first definition because there are documents, moral codes, rituals etc. that provides a structure to the religion.
It doesn't meet the second definition because there is no structure of people. The structures of people are found on a lower level, where we have the religious organizations. They usually have some kind of leadership and a hierarchy and they interpret the content of the religion. These organizations are not mandatory, you can belong to one, or several, or none. You can go from one organization to another.
They actually can have many purposes (expansion via conversion, worship of a deity or deities) which individuals are organised around. The Aberhamic faiths are actually rather specific in this regard, for example Muslims have the Five Pillars of Islam which the group (followers) are organised.
That is a structured content and an organization by the first definition.
Religious followers may organize themselves around some religious content, but when they do that they form an organization that is separate from the religion. A religious organization's interpretation of the five pillars, for instance, does not change the content of the actual religion, just the content of that specific organization and their specific followers.
Christians are followers of the anointed one (to given it the translated meaning), a group of people who follow the teachings of Christ (a common purpose - to follow the teachings of and live according to those teachings).
There may be groups and there may be individuals, but it's not a structure of people because they don't work together. A bunch of people all over the world believing in global peace but being unaware of each other does not constitute an organization. There are people, and there is a common goal. But there's no structure to the people. (And it's not even certain that they have the same goals because their interpretation of the content may be very different from each other.)
The anglican church is an organization of people, because they have a structure of people and a hierarchy, they have a common goal that they work towards, they have formal (and informal) methods of making decisions for the organization. The catholic church is the same. Christianity, on the other hand, is not an organization of people - it's just a set of ideas.
The Soviet Union was an organization, but communism isn't.
FIFA is an organization, but football / soccer isn't.
The Berlin Philharmonic Orchestra is an organization, but Beethoven's 5th symphony isn't.