I have rather strong views on this subject so please take my opinions with whatever serving of salt you like.
That said, I love right click in the browser. When I am on the desktop and working within a web application (Google Dive for example) I often find myself right clicking and seeking to perform an action. And often times - especially when operating within a web app - I am disappointed to find limited or no functionality nestled away in that menu.
That said, I don't believe you should ever have to right click in a web browser for any reason. And for our touch only friends this can be especially frustrating.
So, my approach when designing web applications where I could see benefit of adding a right click context menu to some portions of the app is to first design the interactions so that they can be accomplished with no right clicking whatsoever. Once that is done, if I do believe that some significant portion of users will find benefit from a right click context menu and there is enough time and resources to properly implement the menu, I say go for it!
I hold this same view on keyboard shortcuts. A lot of users don't know about them or care to use them, but for some certain power users they sure make life easier and work quicker.