The push-up overlay menu, visible in the upper right corner, uses the popup feature of Elementor builder.

Popups are call-to-action modal windows that popup and overlay the page at a specified moment or under specific triggers and conditions. Popups are designed to focus a user’s attention once they have taken an action.

To begin, navigate to the Toolbar > Edit with Elementor > Menu Popup/ Hamburger

Or go to Templates > Popups > Menu Popup/ Hamburger > Edit with Elementor. Control the layout, conditions, rules and styles of the popup, and then design the popup content. 

Please check these guides for further information:

Guide to Vamtam Elementor Builder