You have to first CROP in Develop to 16:9 aspect and then you can Export it as a 16:9
Trying to specify a specific dimension in the export dialog won't work if the image isn't cropped properly. You need to crop your images using the 16:9 aspect ratio setting. Then export your images specifying the long side being 1920 pixels. The resulting exported copies should work perfectly.
As general advice (for Lightroom)-
The 'Re-size' dimension options in the export dialog should be considered as dimension "upper limits".
Lightroom will always FIT the image within the dimensions entered in the Re-size panel- regardless of its original pixel dimensions.
For the OP- the 4:3 image will have to FIT within the dimensions 1920x1080, but it will still be a 4:3 image- just re-sized down to 1440x1080.
As in the posts above- For a 16:9 image, it must first be cropped to the 16:9 ratio in the Develop module crop tool. Then it can be re-sized down and will FIT (and FILL ! ) the 1920x1080 pixel dimensions.
"1438" is just a slight 'glitch' in the re-size.