GEE Export.image.toDrive output not matching bounding box?

When you apply the clip method to an Image, all you are doing is masking out pixels outside that geometry, but your NDVI image is unbounded. If you want to export only one region, you have to use the region parameter in the exporting function. An in this case it's easier to pick it up directly from your FeatureCollection

// Export image
Export.image.toDrive({
  image: NDVI,
  region: geometry.geometry().getInfo(),
  description: 'NDVI_S2_Aug2018_2',
  scale: 10,
  maxPixels: 10E11,
  fileFormat: 'GeoTIFF',
});

Also, make sure you are zoomed out from the image area. If you are zoomed in past the edges of the polygon you are trying to clip to, only the contents of your map window will be exported.