Gmail on OSX Right Click
You can't change the contextual menu (activated by Control Click or "Right-Click") because it's embedded within the App; this includes the HTML code of a web page.

From Apple's Developer Documentation


  Contextual menus pop up when the user Control-clicks or right-clicks
  over an object. Safari presents different contextual menus when the
  mouse pointer is over the toolbar, Bookmarks bar, an extension bar,
  the tab bar, or the contents of a webpage.
  
  Your extension can add menu items to the contextual menu that pops up
  over web content. You control the actions of the menu item by
  installing a listener function for the "command" event in either your
  global HTML page or in an extension bar.


(Emphasis mine)

Essentially, what this is saying is that the developer of the (web) app sets the contents of the contextual menu.  If they don't set it, it will be the default for whatever is set in Safari/Chrome/Firefox/etc.

If your goal is to open a link in a new tab, hold Cmd while clicking to bypass the menu.  Holding Shift while clicking opens the link in a new window.  I have found these options quicker than right clicking as my left hand rarely leaves the keyboard and I don't have to parse through a menu to find the item I want.