It is not result of a registration, it is just a tilted-gantry CT acquisition. In such images, axes are not orthogonal.
The main question if there is a way to write a tilted gantry acquisition (non-orthotonal axes image) into a Nifti file that is interpreted correctly by all modern Nifti-capable applications, or it is safer for ITK to refuse writing of such images into Nifti.
Based on what I have learnt from the answers here, it is probably better if ITK’s Nifti IO refuses writing images with non-orthogonal axes.