This solution enables you to link the featured image displays using the genesis featured posts widget to the 1st category the featured post is assigned to.
The code creates a custom featured posts widget which appears on your widgets page.
The custom featured posts widget is named Category Linked Featured Images and is created in addition to the default genesis featured posts widget.
Once you install the code, you can then modify the code in the file which adds the widget.
Here’s the code for logged in members: