Is there a way to set search results in Responsive HTML 5 output to eliminate the descriptive text?

To hide the description/context in Responsive output, you'll need to inspect the output to determine the correct css, add that code to a custom css file and add it to the skin in the User Assets section.

Exactly what the css is will depend on your RH version and skin.

This thread includes some information about how to hide the URL/breadcrumbs (scroll down past the initial information for Frameless skins) which should give you an idea of what to look for:

https://community.adobe.com/t5/robohelp-discussions/in-rh-2019-search-results-is-there-a-way-to-hide-the-file-path-for-results-please-help/m-p/10929089#M128843

Other customisations may be possible but you'll need to play with the css to see if you can do what you want.