Note that https://thebettervacation.com/web-stories/ is an archives page as provided by WordPress by default and as designed by your theme.
Your theme displays contents in archives with both their featured image (cover image) and an excerpt.
What the Web Stories plugin does it replaces the excerpt with the story player. Hence you see the these things twice.
Here’s what I’d recommend to do to improve this:
– First, reach out to the theme developer to ask them about improving the archives layout for web stories
– Second, add the following CSS to your Additional CSS section in the customizer to change the layout yourself in the meantime:
To hide the cover image:
.post-type-archive-web-story .type-web-story .post-gallery { display: none; }
To hide the title:
.post-type-archive-web-story .type-web-story .post-title { display: none; }
To hide the interactive story player:
.post-type-archive-web-story .type-web-story .post-excerpt { display: none; }
Apply them as you see fit.