That’s their main website and not Discourse though. The code I helped them with was for Discourse only, which doesn’t scale down to that menu either.
In short, you would need minimally add more HTML. You would have to have a menu (that is hidden at larger viewports) plus the horizontal menu which is visible at larger viewports. Then as the viewport shrinks your CSS media queries should hide the horizontal menu and make the menu visible.
This is a good read of the concept behind what their main site is doing