I think the assumption being made is that you have copied the entire style.css from twentyfourteen over to your child theme folder, and started modifying it there. Like you, I have only added the styles that need to be changed instead.
Once I added a functions.php with the code provided in the thread I linked to above, I realized that it prevents widgets from being placed in the sidebars, but does not prevent them from being rendered - that has to be done using the css.
Next, I looked for the code to be replaced, and found it in the 11.0 Media Queries section of the original styles.css file at line 3216. At this point, I decided to learn more about media queries in order to learn how I could apply this code to my child theme without copying everything over. This page explains how media queries work, and it is quite helpful.
I think the trick is to put the appropriate media query into your child theme css above the replacement code, and it will override the master theme code depending on the width of the browser window. I will try it and see how it goes.
As a novice at this, I welcome any input from those who really know this stuff!