Notice that corporate management has in this example identified and developed the concept of, as well as defined the requirements (task / mandate) of the project, including the mandate of project management. In addition, Corporate management is responsible for setting up and implementing the management of this project (allocating people, office, resources, etc). This can be done quickly since in most companies there are accepted project management practices.
However, the actual service delivery of a project is normally designed and built by the project manager, not by Corporate Management who set up the project. This is shown in the diagram by the arrow from the operation of project management to the specification, design and implementation of the project.
Note that there is a slack terminology used by many people mixing the words 'project' and 'the product of the project' thus not being able to talk separately about the life cycle of the project as opposed to the life cycl of the project's product E.g. the product of this particular change project is the set of deliverables that describe the specification and design of the Manufacturing Division.
So, the project manager creates the requirements specification of the project (i.e. what are the processes/activities that the project must perform and when [usually a process diagram plus a GANTT chart are used to do this]).
The project manager also designs the project, by determining how the above process will be allocated to various project teams and roles, and what automated resources will be used to perform some activities of this process. The project manager then also does some detailed design (if necessary) of the above and finally the project manager 'builds' and 'releases into operation' the project. What we mean by building / releasing into operation is the building of project teams and allocating/ hiring, training people so that finally the project teams can actually start its operation.