Adding Data Catergories

Can an "author" add data catergories?

I have a comparison table which is a responsive HTML table and when you look at it on mobile view it has headings which are created using data catergories

https://www.greatestreviews.co.uk/best-tens-machine/

you can see here it working ^

But when i have someone adding the content for me as an "author" and not "administrator" they can add the HTML but when you go from the HTML editor, to visual then back to HTML editor the data catergories seem to disappear.

I'm not sure if this is a theme issue, a browser issue or because its because the author isn't allowed to add HTML.

Any ideas?