Actually scratch that. I believe I have found the issue preventing the shortcodes from being processed. It does not appear to be caused by the theme or another plugin, so the troubleshooting steps previously suggested are not necessary.
You have some invisible ‘-
‘ characters in your code. When I copied the shortcode block from ‘view source’ on your page and pasted it into a text editor, the result looked like this
[--tabby title="Thanksgiving"--]
stuff
[--tabby title="White Wine"--]
stuff
[--tabby title="Red Wine"--]
morestuff
[--tabbyending--]
These invisible charactes are intended to prevent the shortcodes from being processed in the page in the example on my site are surviving being copied & pasted into your site.
The fix will be to delete that block and retype the shortcodes manually.
I have changed how I format the the example shortcodes on my site to use character codes for the square brackets rather than typing them with the invisible character, so this shouldn’t happen again if anyone copies the code rather than typing it.
Please let me know whether this fixes it.