Why is the secondary winding of a current transformer shorted?
Any resistance on the current tranformer secondary will be transformed into resistance on the primary by a factor of \$ \frac {1}{n^2} \$ where \$ n \$ is the turns ratio. To minimise the primary impedance you need to short the CT secondary.

You may find it helpful to consider CTs as complimentary to VTs.


VTs are happy with secondary terminals open-circuit. They are then unloaded.
CTs are happy with secondary terminals short-circuit. They are then unloaded!
VTs do not like short-circuits on the secondary.
CTs do not like open-circuits on the secondary.



  Or is there perhaps a definition of 'shorted' which refers to something other than a low resistance path?


Nope. Use the best short-circuit you can make.