De Beers certainly had government help. The paper used by Wikipedia to support the claim that they are considered a monopoly[1] acknowledges this:
> In addition to the structure of the De Beers cartel, the main force behind this dominance for many years has been the role played by governments. It is possible for a cartel to continue if there is a governing body above that can enforce agreement. Through continuously changing its stance toward corporations, the South African government and other governments essentially protected the companies that were providing them with easily and centrally collected tax revenues. Governments have frequently imposed output quotas and have used legislation, such as the Illicit Diamond Buying laws (IDB), to protect these companies from black markets and their effects on pricing. (As a comparison, one of the weaknesses of OPEC is that it is a cartel of governments over which no other actor can impose control, whereas De Beers has formed a cartel of companies and has often successfully lobbied governments to enforce cooperation on its behalf).
> This argument of government-forced cooperation held while Africa was the dominant supplier of diamonds, but it no longer has the complete stranglehold that it once did. As the cartel has not yet disintegrated, however, other reasons must also exist. Researchers believe that De Beers exists as a monopoly to maximize profits, not just to maintain them. Hence, it is in the members’ interest to stay within the cartel rather than go it alone.
It's however conceivable that a monopoly like De Beers could survive even in a free market because they seem to be the optimal solution to a coordination problem where everyone's (including the consumer's and the prospective competitor's) incentives are aligned. The paper explains:
> Second, the demand for diamonds is not typical and must be analyzed using Veblen’s theory of conspicuous consumption. This theory replaces the traditional downward-sloping demand curve with one that is upward-sloping, suggesting that the higher the price of an item, the higher the demand. This phenomenon would imply that higher prices have a dual effect on the profits of a company, first, through higher margins and, second, through increased sales. Therefore, it is in a company’s best interest to maintain high prices. For diamonds in particular, this means that the perception of desirability associated with diamonds is critical to the life of the industry as a whole and that if the price of diamonds falls, the overall demand for them will follow. Therefore, it is again in the interest of the individual players in this industry to “play nice” and cooperate, since cheating the cartel will actually lower their profits instead of raising them.
[1]: https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfile...