It might be easiest (IMHO) to recreate this from scratch simply by creating a 100% width 100% height div that has Position set to Fixed, z-Index set to a higher number than any other z-Index setting on your site (like... 1000 ) and a dark background color (perhaps with .9 opacity on the color so you can kinda see through it). Place your links in a list and position/style them as you like.
You will then need to copy and paste the menu open button and ensure it is in the same exact spot within your menu div. Use interactions on the "normal" menu button to affect different element (that element being the div) and sets the visibility of the div to visible, then the opacity to 100% with a fade transition time of 100ms. You will then need to use interactions on the button inside the menu div that affects different element (again, that element being the div) and does the reverse of the last interaction you just made. Make sure your "first click" setting is set to LOOP so the clicks can be done over and over and over again. Note: neither of your menu items need a second click interaction, just FYI.
I built something similar for a client that can be seen at Wish Dish - all from scratch.
This takes time, so approach it with patience and you will succeed. I believe I've included all the details you need. As for mobile, you can also accomplish this effect but will need to shrink down your links and make sure your button is in good placement (upper left or right corner of topbar) and it should be beautiful.
Wishing you the best on your project