The answers to the clues start at their letter and go straight across the web, ignoring the hole in the middle. The hole really is not important in this puzzle.
You also have to solve the Slitherlink.
The outside row of the web reads FULLY STICKY SQUARES. The flavor text identifies the Slitherlink path as the "safe" route of non-sticky cells, so identify the grid cells that have no part of the path adjacent (the cells that can be marked as 0 for Slitherlink purposes). Those, reading clockwise and centerward, spell the answer, RADIO SILENCE.