Good question.
Start with this, though. The Times has two classes of stock -- Class A and Class B. Class A is publicly traded. Class B is privately held by the Ochs-Sulzberger family.
Both classes share in the profits, such as they are. But Class B nominates 9 of the 14 directors, thus controls the company.
It's not said whether Slim and Proto gained control of 19% of the Class A or Class B shares -- though I presume it is the former, since they say they are now the company's principal shareholders.
My guess is that Slim has plans. Note that Proto, who has a minority stake (just 2%) also owns the leading Italian newspaper -- Corriere della Sera. Proto is probably partnering with Slim for his newspaper expertise.
The odd thing is that the New York Times brand may have more value than the actual operation. They might have some plans to exploit the brand in some way, while they try to keep Pinch & the boys above water.
This isn't going to turn the Times into an anti-American internationalist tool any more than it already is. Meet the new boss, amigos.