I have the following HTML page (page is simplified here as it is a sample of the real one):
No. Getting links by getElementsByTagName("a") is your one-off web-developer solution.
You can also traverse the DOM properly by childNodes, and this solution generalizes to all UL lists you may have:
_($("#my-list")[0].childNodes).filter(function(node) { return node.nodeName == "LI"; })
It uses underscore and jQuery.