The primary advantage
of mouse gestures is, that you can keep your hand on the mouse
. Thus, you lose no time switching between the mouse and the keyboard
, which is annoying
Especially for viewing websites this comes in handy, because you usually don't need to type text anyway. And with a scrollwheel-equipped mouse, the user experience gets even better. All the usual actions, such as following a link, reloading a page, go back/forward in the history, close a window, open a new window, etc. can be performed while keeping your hand on the mouse, ready to click on links. Also, it helps one handed surfing.
The cenceptual sister of mouse gestures is called pie menus, which also aid in the act of one-handed browsing but operate in a way more similar to that of a traditional menu in the ubiquitous WIMP system.