If you have a friend who wants to succeed at a task, or needs healing, and he asks you to pray for him even though he can pray himself, is he using you as an intermediary, like shitoof? Am I confused on the definition of praying for someone and shitoof?
שיתוף does not mean "intermediary." In fact, it is a common Jewish practice to ask an intermediary who one sees as more worthy of having his prayers answered to daven for something. This is one of the roles of a chasidic rebbe, for example.
The concept of shituf is ascribing partnership to God. The word literally means "grouping." It is forbidden to claim that there is another deity that has the same level of power as God or who works with God.