The primary stuff you need to form stars is hydrogen and helium which is absolutely everywhere in the universe. In order for stars to form, however, you need a lot of it. This usually happens if you have a strong gravitational force, which pulls in more and more gas (very very slowly). If the gas cools sufficiently, at some point the gravitational force will overcome the thermal pressure of the gas, causing it to collapse and form stars.
This is the basic mechanism of star formation everywhere and it probably isn't much different in this particular system. The strongest gravitational forces are caused by dark matter haloes which are usually larger than the galaxy itself and much heavier. On smaller scales, the main gravitational force is caused by the collapsing gas itself. Both probably still exist in this system and provide the required gravity for stars to form.
A note: While dust has an impact on star formation (it might help the gas to cool, for example) it is not a required ingredient for stars to form. In fact, the first stars formed at a time when there was no dust in the universe.