You can hide Hangouts in the Gmail web version and here’s how:
Sign in to your Gmail account.
Hit the Gear icon at the top right.
In the menu, hit Settings option which you can find between Configure inbox and Themes.
Navigate to Chat tab which you can find between Add-ons and Advanced.
Select Chat off.
Hit the Save Changes button.
Note: If you want to show Hangouts, then follow the above steps, and instead of selecting Chat off, choose Chat on.