The menu on that site would be dead easy to replicate, just use two different menus, styled accordingly. Allow one to scroll off the page as normal, put the other in a chroma set to slide down triggered by a marker, with the marker below the menu that scrolls up.
I use a different menus below the breakpoint (opposed to a mobile version of the full width one) on a lot of site, as that way you get much better control over the mobile version. That Mailshot Monkey site uses a different menu above and below the breakpoint. If I used the desktop version for the mobile version, the links that on desktop are drop downs on mobile would require a click to see them. Most mobile menus handle drop downs this way, but it’s daft, as on mobile you’ve loads of space for lots more items.
Point in case: That UChicago website you linked to has a mess for a mobile menu. Some items are duplicated from the top of the homepage in mobile view, and as you click into the mobile menu, there is no way to back a level.
I reckon most people who make mobile menus totally fail to consider the situations they’re used in. They test them sitting at their desk with both hands available, but fail to realise a large portion of the user base will be using them on the move, perhaps one handed, in a rush, in less than ideal environments.
IMO 90% of menus are poorly thought out in general, and almost all menus available off the shelf for RW are the same. The menu is the single most important aspect of any website, yet it’s about the most overlooked element on most RW sites.
Just my opinion.