You need to indicate somehow to the system that the specified user is allowed to view all requests of a single process.
Without adding the user to a participant: He/She either needs to be an administrator or a process manager.
Otherwise, the user has to be a supervisor. But you need to create a participant for that. This participant does not need to be involved in the workflow, it’s just enough to change the type of that participant to supervisor and all users of that participant will be allowed to view all requests of the desired process.