" When machines and computers, profit motives and property rights, are considered more important than people,..."

The chain, the whip, and the sword mirror Dr. King's "giant triplets of racism, extreme materialism, and militarism."

The chain is prison, criminal records, and credit scores that keep people bound today. Like race in the time of slavery, they obscure the humanity of the person.
The whip is the terroristic threat of economic hardship to the point of death that can be wielded over people in workplaces where there is less and less protection for democracy, dignity, and stability. It is the logic that people must be coerced in order to work.
The sword is the timeless militarism of which Dr. King spoke.

This logic, this way of looking at the world, creates the very criminals, failures, and violence those who seek to justify it set out to find, while a tiny group reap vast profits from it as they sit besieged in a world of misery. The lesson of slavery's failure has been slow to sink in.

There is another way: see the economics section.

Historic Background

The first chapter of Steve Reich's book captures the period in which Dr. Kings insight into oppression is rooted: the time when the US struggled with the end of slavery, and how to move forward. Citing the report of William E. Strong on Southern planters to Major-General O. O. Howard, January 1, 1866, "Reports of the Assistant Commissioners," Sen. Exec. Doc. 27, 39th Congress, 1st Sess., p. 83, Reich quotes:

They insisted that unless they resorted 'to the overseer, whip , and
hounds' their estates would deteriorate and never recover.
... "Planters resented that emancipation not only challenged their
sense of racial supremacy but also eroded their authority as employers
of labor." p. 13

The fate that awaited African Americans was one with which many workers of all background can relate today:

"Because black material success often rested on white goodwill, blacks
took great care not to appear too successful or to transgress racial
boundaries"

Reich goes on to tell of a black teacher who felt compelled to live in an unpainted house. p. 39

Reich spells out the details of the political reasoning at the time.

"The political activism of black workers in the low country caused
Republicans to fear the African Americans would corrupt the political
system by seizing the reins of government in order to confiscate
property, redistribute wealth, and erode the promise of social
mobility through hard work. Faced with growing whit working-class
unrest in the North and politically mobilized former slaves in the
South, Northern Republicans abandoned their working-class allies,
fearful that they would sow the seeds of political and economic
disorder by strengthening the rights of labor at the expense of the
rights of property." p. 30

"Many Republicans, who valued property rights over labor rights, grew
fearful of encouraging a class politics from below. More and more,
they became convinced that it was safer and wiser to come to terms
with former Confederates than to promote and protect the interests of
their black working-class constituents. In so doing, they enabled the
whit propertied elites of the South to survive the trials of
Reconstruction." p. 31

Quotes from A Working People: A history of African American workers since Emancipation, Rowman and Littlefield, 2013, New York.