I know this is an old-ish post, but in case you or anyone else is still looking for an answer:
In the following example I am using a heightmap of a terrain, but that should not matter all that much.
This issue might be related to the UE version you are using.
When I try to import this 16 bit PNG:
I get the following results:
[UE 4.26]
Drag and drop the image into the Content Browser and double click it to open the Texture Editor.
Under “Compression Settings” you can select “Grayscale”.
When you now click “Save” this should result in a “G16” image, however in UE 4.26 the result is: