How is starch content of some vegetables reduced by cooking?
Starch is a polymer of glucose.  To use the glucose you need to break pieces off the starch.  Starch concentration decreases as the starch molecules are broken up.  


source

This is hydrolysis, because water is added to break the sugar molecules off.  You  need acid to help, or enzymes like amylase.  Some vegetables have amylase in them which they intend to use to process their own starch.

As starch content decreases, free sugar content increases.  The free sugars are broken off the starch.  This is stated in your linked source.