I am not familiar with GeoTIFF, but it seems several elements are missing from the file. Perhaps WL is expecting them to be present? The error message $Failed is not very informative. You should report this to Wolfram Support.
elements = Import["~/Downloads/Test.tif", {"GeoTIFF", "Elements"}]
AssociationMap[Import["~/Downloads/Test.tif", {"GeoTIFF", #}] &, elements]
