Not only is this differentially private, it's locally differentially private, which is an even stronger privacy definition. It's "local" because the user adds randomness themselves. Generic differential privacy is a weaker definition because it lets whoever's running the algorithm collect raw data and then add randomness somewhere in the computation pipeline to produce privatized outputs.

This kind of example also predates the definition of differential privacy by about 40 years [1], although the motivation is pretty much the same.

[1] https://www.jstor.org/stable/2283137?seq=1