Competitive authoritarianism is a term introduced by political scientists Steven Levitsky and Lucan Way in "The Rise of Competitive Authoritarianism," published in the Journal of Democracy in 2002. It describes hybrid regimes that maintain significant "arenas of contestation" between incumbents and opposition, but in which incumbents violate the rules so often and so seriously that the regime counts as a subtype of authoritarianism rather than of democracy (NED, Journal of Democracy Classics).
How such regimes arise
According to the authors, competitive authoritarian regimes can emerge from the decay or collapse of an authoritarian regime, or from the decay of a democracy, and can afterwards move toward either more democracy or more authoritarianism (NED). That two-way movement is why the case studies on this site distinguish countries that are consolidating from those, like Hungary and Serbia, where voters have recently pushed back.
Relationship to the playbook
The concept explains why the Seven Pillars focus on tilting the playing field (capturing referees, pressuring media, manipulating electoral rules) rather than abolishing elections outright. For the related idea that this tilting is increasingly done through formally legal means, see autocratic legalism and stealth authoritarianism.