Link to study: American Academy of Neurology
After adjusting for factors such as age, sex and race, as well as health-related factors such as high blood pressure and diabetes, researchers found people who had been taking acid reflux drugs for more than 4.4 years had a 33% higher risk of developing dementia than people who never took the drugs.
The Vox article does a better job of communicating the findings without the hyperbolic headline. The study wasn’t explicitly designed to look for association. Nonetheless, the data is there.
Neither study does a particularly good job determining causality. The higher quality study was limited in time (3 years) and participant age but perhaps the findings also broadly apply.