I tried the same conversion tool with other skinned mesh i found online (cesiumango.dae) and it worked well.
So something goes wrong with this model specifically.
I suspect there is some tranformation issue involved.
Does your DAE file work when you upload it to sketchfab.com or clara.io? And what happens when you upload the converted glTF file to one of the mentioned websites?
If the glTF model does not work, you should post an issue here. Collada is quite complex and maybe the converter misses something…