There isn’t much going on in that sidebar: 2 menus, archives and an ad. It’s also not widgetized, you can’t do anything more than that into it. If you don’t have a 24 inch screen you will still view those things, but not as a sidebar.
Also you need to be exactly above 1600px. If you want you can decrease the media queries. In style.css find:
@media screen and (max-width: 1600px) {
replace 1600 to 1550 or something. Also in ../assets/js/myscripts.js
do the same with:
if( $(window).width() >= 1600 ) {
I didn’t try it, see if it works. If you really need that sidebar you can always hire a freelancer and code the all thing again.