How to make table-responsive in drupal views
Consider the Views Responsive Grid module. Here is a quote about it (from its project page):

... provides a views plugin for displaying content in a responsive (mobile friendly) grid layout. Rather than trying to force the standard Views grid display to work for mobile this provides the same functionality, but in DIVs instead of tables. Provided is also the ability to specify a horizontal or vertical grid layout which will properly stack the content on a mobile display.
Features:

Horizontal or vertical grid layouts
Custom classes for use with responsive themes


Of course, this requires the use of a contributed module (which is something you want to avoid as per the edited version of your question).
Assuming that it's OK to use a contributed &quot;theme&quot;, you may should consider using a responsive theme, such as (popular) Omega or Zen themes. There is also the Beep Edition &quot;theme&quot;, which (quote from project page) &quot;is designed from the ground up as a mobile-first responsive theme&quot;. However that has like 5 module dependencies ...
For a list of way more (less known) responsive themes, refer to 26 More of the Best Responsive Drupal Themes. Quote from that link:

All of these free Drupal themes have responsive layouts, and they include great features like Bootstrap frameworks, Google Fonts, sliders, Font Awesome icons, Facebook integration, social networking icons, and more.