First of all, there was no material change in the law, this is a misunderstanding (to some extent a misunderstanding intended by the author) of what is being explained. The change being discussed is actually a change in how economists and corporate law theorists think about corporations.
The basics of corporate law did not change significantly in the 1970s. There were some minor changes starting to take place then in law and practice, however.
The most notable of these were the rise of insider trading laws with real bite, the innovation in financial practice of the leveraged buy-out which precipitated "poison pill" defense from board of directors, and the surge in CEO pay often in the form of stock options.
There has been a shift in perspective and framing of the issues, but these changes are not huge changes in corporate law per se. Legal decisions allowing "poison pills" were minor anti-shareholder rights innovations. Tax laws encouraging stock option compensation were minor shareholder value oriented innovations. The theoretical basis of insider trading laws is a doctrinal muddle. No one conception of the corporation is completely dominant today and drives all legal theory and policy decisions.
Secondly, Lynn Stout is engaged in a misleading bit of ret-con in her article and is presenting a misleading history of the evolution of corporate law scholarship.
This history, by the way, isn't terribly old. The right to form a corporation without a specific piece of authorizing legislation of the kind that creates a government agency, for example, is only about 150 years old or so, and both internationally and until quite recently, was much harder to form (e.g. many countries, such as South Korea, require proof that a corporation has insurance in place and sufficient capital to pay its debts before it is allowed to incorporate - corporate law firms still face some of these restrictions in the U.S.) Before then, each corporation was an individual legislative concept to some extent.
The notion that corporations should maximize shareholder well being, because they own the corporation, is the older and traditional view. Milton Friedman and the authors of "The Theory of The Firm" were simply restating the consensus view in a more focused and economically defined manner, not innovating. These pieces were published as apologies for that traditional view once it started to be challenged.
The view of a corporation as a web of contractual relationship with bondholders, suppliers, employees, customers and shareholders is the more modern view that started to gain currency sometime around the 1960s and 1970s, which is why people like Milton Friedman felt the need to articulate a defense of the traditional view that had previously merely been assumed and gone unchallenged.
The web of contracts theory was articulated initially to a great extent by corporate law theorists seeking to provide a theoretical justification for corporations to act in a responsible manner that treats its employees well, behaves honestly, goes above and beyond its legal obligations to honor the spirit as well as the letter of the law, etc.
Some of the most notable corporate law responses to that theory are the law of publicly held companies in Germany, which requires that employees have a minority number of seats on the board of directors of a company, and the laws in some Scandinavian countries that call for rough gender parity on corporate boards of directors. There have also been a smattering of laws passed at least authorizing corporations to consider factors other than profit maximization.
Another related version of corporate theory to the web of contract theory is the "director primacy" conception of the corporation that sees a corporate board of directors as the hub of that web of contracts and the body which corporate law should protect the power of. Professor Stephen Bainbridge at UCLA Law is one of the leading proponents of this minority view of corporate law which was starting to emerge in the 1980s to justify efforts by corporate boards to defend themselves from the emerging threats of leveraged buyouts and proxy fights.
Bainbridge's view is nonetheless significant because it is an overarching theory that explains a variety of major corporate law doctrines, particularly in Delaware, whose law is dominant in the governance of publicly held corporations, that seem to be at odds with a shareholder primacy view of corporate law. It can explain the legitimacy of both "poison pills" and large CEO pay packages, the Delaware court's hostility to derivative suits, and its hostility to shareholder activism. To some extent, the "director primacy" view of corporate law is the web of contracts theory twisted and seen through a conservative lens that uses the theory to urge the law to crush the kind of shareholder activism for social good and employee rights that the original web of contracts sought to advance.
The rights of everyone other than a shareholder in a corporation are simply contract law rights - bond contracts, purchase and sale contracts, employment contracts, etc.
The web of contracts theory argues that the legal rights of shareholders vis-a-vis a corporation really aren't that different and that this relationship is really more like any other contract right rather than really being a genuine ownership relationship like the kind of ownership someone has over their other property that should be entitled to special consideration.
This view has a lot to do with the fact that in publicly held companies, in reality, shareholders have no meaningful role in the governance of the corporation or selection of members of the board of directors via the occasional Soviet style ballots for directors that they complete. Instead, in this context, shareholders apply the "Wall Street Rule" and sell stocks of companies that they feel are ill governed and don't worry too much about their practical inability to compel dividend distributions since they can take profits from retained earns by selling their stocks. This makes them look more like people with any other commodity to trade with purely contract and not political/ownership rights. This view doesn't translate well to closely held corporations where shareholder governance rights, in practice, are much more meaningful.
Also, for completeness, it is worth noting yet another emerging view of corporate law theory, developed mostly by liberals who favor campaign finance restrictions for corporations and want to restrain what they see as abuses of power by big business. This is the anti-corporate personhood movement that questions the assumption of all previous theorists that corporations should be treated in most respects as a "person" under the law.
For what it is worth, in my opinion, this movement improperly conflates abuses and power divisions that arise from businesses being very large and those attributable to the corporate form of business organization itself which actually can be very helpful in regulating businesses and redressing the harms that individuals suffer from corporate activities, by making it unnecessary to identify who within the corporation in particular causes a harm attributable to the corporation in litigation and regulatory contexts.