Exactly. Well not exactly. The desalinization plant produces brine (very salty water) as a waste product. Rather than disposing of it directly, they use the brine to generate electricity. This electricity is then used partly to run the desalinization plant.

As an imperfect car analogy, the way a turbocharger uses energy from the exhaust to inject energy into the intake, in the form of compressed air.

Neither is a perpetual motion engine, but both make the useful work more energy efficient.