The command -average_files and -median_files were indeed buggy with 16bits files. This should be fixed now, after an update of the G’MIC commands :
$ gmic -update
(I assume you are using version 1.7.5_pre, otherwise, it won’t work).
After the update, computing the average and median of a sequence of 16bits tiff should work as expected.
Also, please note that by default, G’MIC saves .tiff files as 32bits float-valued files, and unfortunately, there are very few viewers that recognize this format (it is still a mystery for me, as this is a legacy tiff format).
You can force the output tiff files to be saved in 16bits in G’MIC, by specifying ushort after the filename, like this :
$ gmic -w -median_files test16bits\*.tiff -o result_16bits.tiff,ushort
Let me know if all work as I hope it will 