It's not necessary for git, no. However, it's a really good habit to get in—you make some changes to the project and then test it locally before pushing your changes to your git repo (on github and/or elsewhere). This way, you make sure your changes didn't break something that was previously working.

Now as to why start the simple http server to check your work vs. opening the index.html file directly in the browser:

1) relative links can behave in an unexpected manner using the file:// path, and you'll get more consistent behavior using the server

2) There are sometimes permissions errors loading scripts into the page when it's displaying through file:// (relatedly, protocol relative links eg. //code.jquery.com/jquery-2.1.3.min.js won't work).