A few problems here.
First, a wise sensei onbce told me to always format my tables properly with <thead> and <tbody> tags. DataTables also expects you to do this otherwise it will fail.
Second, the ads.js.coffee contained lines configuring non-existent columns. Removed those.
Third, application.js.coffee had a require_tree - you don't want this because you have js files in data_tables folder that you do not want to run as executables, but rather to be available as libs to be called as required. I commented it out but should delete it.
Fourth, the jquery_ui gem was missing - not sure that made any difference but I'm sure you'll use it soon.
Fifth, I also added the asset precompile config to production.rb for eventual deployment.
Sixth, DataTables doesn't deal well with headings that have colspans - which of the subcolumns should be sorted/searched? So I removed the colspan and collapsed the 3 columns to one.

I had forgotten how much fun DataTables was! I love seeing it work!