Here's a .hype document from the solution above:
Hamburger.hype.zip (15.4 KB)
It appears the screenshot also has a little bit simpler of a method. The general trick is that you will want the timeline to animate both opening and closing. You'd add a timeline action at the halfway point that pauses the timeline. Then the button itself would just be a 'continue timeline' action with 'Can restart timeline' checked.