Yeah, that produces a sine wave, but it’s fixed frequency and (I assume) has a manual or no gain control. The fixed bank I linked to uses roughly the same circuit, but with a bit more components to manage gain.
To make an adjustable wien oscillator, you need to change two resistors at once, and you also need to manage gain – it needs to be 1× for the best wave form, but higher at first because otherwise it won’t start oscillating. Figuring out how to do that, and without introducing too much distortion, was a big topic some 90 years ago, and made some people rich: