To the extent they know it at all, the state currently occupying America’s political attention is probably most familiar to Chinese people as the place where their president went more than three decades ago to learn about animal feed. But that isn’t keeping China’s state-run media from using Monday’s Iowa caucuses to deliver a quick lesson to their readers on U.S. presidential politics.

A handful of official Chinese media outlets offered previews on Monday of the opening contest in the 2016 presidential race, attempting to...