Unfortunately, the web version does not provide the option watch Instagram stories from a computer (maybe for now), but you can solve this problem using the extension for Google Chrome called Chrome IG Story. You not yet use this browser? That’s just the reason it appeared to deliver.
Download Chrome IG Story here. After installation look for its icon in the browser control panel next to others extensions.
By default, the extension offers Stories from Instagram profiles celebrities, but by search you can find any user at all and see his stories from the computer (if a person has an open page).
And this button will provide you with viewing in a separate window, so convenient.
By the way, did you notice the Download icon below? Yes Yes, stories can be downloaded (and here is another way how to download)! Click on this button and the archive with all stories of any user Instagram (provided that he has an open profile, of course) downloads to your computer. The archive will contain both photos and videos in mp4 format.
You can search for stories by tags and locations, for example, you can watch all stories from a city or place, which you are interested in, as well as those who are assigned a certain hashtag sticker. In addition, live broadcasts are also available to you (tab “Top Live”).