There are two aspects of the Harvard Charter which may give standing. First, the endowment has a specific purpose: "be for the advancement and education of youth, in all manner of good literature, arts, and sciences." And, good sciences say that investing in fossil fuels is a bad idea. Second, the Harvard Corporation is established so that it may be sued: "and also may sue and plead, or be sued and impleaded by the name aforesaid, in all Courts and places of judicature, within the jurisdiction aforesaid." http://library.harvard.edu/uni... So, disagreements about the endowment are supposed to be settled in court.
These are probably relevant, but may not be the ticket.
Standing is a question of *who can sue* (it is rather literal - you have a right to stand up at Court and be heard).
As you note, the charter gives a purpose, a *why*, deviation from which may give rise to liability. But the question is who can enforce. Does the Charter exist to protect the students? Faculty? The institution itself? Its property? Who is harmed by deviation from the Charter?
A relevant phrase might be "that may conduce to the education of the English and Indian youth of this country, in knowledge and godliness" as the *who* benefitting (and hence may have standing) is "English and Indian youth", antiquated racism though that may be. But who knows what a Judge would think or other status may be alive in this case.
The naming of the corporation gives no indication of standing to sue either. It just mentions jurisdiction and by this order, presuming you have standing, the name one would provide the Court to sue and enforce an Order against the corporation as a defendant.