Intercessory prayer seems to me to be a form of magic, but I don't understand how it fits in with the problem of psi phenomena.
There does seem to be a problem with using a word like "magic" to describe psi phenomena. It suggests negative qualities when used by some theists as well as some atheists. Both groups want to claim they are not doing magic, but for different reasons.
The theists, on the one hand, want only their priests or pastors to officiate over orthodox rituals (magic). They want to monopolize religious authority and not share it with "pagan" magicians. The atheists, on the other hand, don't like the magician's subjectivity interfering with their unconscious technology (magic). If atheists want to bend a spoon they will put one end of the spoon in a vise and twist the other end with a pliers. This way they can ignore the fact, because it is too obvious, that they needed their subjectivity to intend to bend the spoon in the first place. The vise and pliers would not have wasted their time doing it without them.
Sometimes I think our very ability to use language is a form of psi phenomenon. We just take it so much for granted, we don't see language as an unusual ability. However, for it to be a psi phenomenon would require some theory of psi that would explain language and also be able to make predictions so the theory could be falsified.