Praise be to Allah.
This co-operative business organization is governed by the same rules as other business organizations: it must pay zakaat on its wealth. What you have mentioned about it being set up in such a way that it has to give ten percent of its net profits to charitable causes does not mean that it is exempt from having to pay zakaat. The ten percent referred to in the question is like voluntary charity (sadaqah), and sadaqah does not replace zakaat, because zakaat is an obligatory act of worship which must be carried out with the appropriate intention (niyyah). This amount of ten percent is not being paid as zakaat; it is being given as a voluntary act of charity. So this co-operative organization has to pay zakaat. And Allaah knows best.