Chrome IG Story is an extension for Chrome that makes the Chrome version of Instagram function similarly to the Instagram mobile app, primarily by creating a set of your friends' Instagram stories above your feed.
Instagram with everything included
The main feature of Chrome IG Story is providing a view of your friends' Instagram stories where normally there isn't one. The sorting algorithm is nearly identical to what you'll see on the mobile app, so when IG Story is available to you, it's expected you'll use it preferentially. It does indeed work more naturally on most desktop computers than the web version of Instagram, and it provides most of its features: you can browse stories from those you don't follow, or download stories with a right click.
Read the stories that people want told
Chrome IG Story is essentially a partial overhaul of the normal desktop Instagram interface. It provides a view that is normally only available, and frequently used, on the mobile app. It also maintains most of the desktop version's functionality or even adds to it. Some parts may not work as expected, but for those who almost exclusively use the mobile app, it should be a natural choice.