I am really surprised because the processing of shortcodes is more of a server side thing than the client. WordPress should convert the shortcodes into valid HTML and hand over the same to the client browser.
The shortcodes themselves are not being processed here somehow for mobile. Can you pls share a temp login pls? I checked the demo site and I see that the tabs are showing up fine on mobile. I will need to check the backend code and also see if removing the video inside the tab makes a difference. Thanks