Sorry, we think we have not explained the solution properly. You can't use CSS styles, because styling checkboxes through CSS isn't supported. You need to use MS Word styles, and this style needs to be applied to the whole paragraph to set checkbox font-sizes. On https://www.phpdocx.com/documentation/introduction/html-to-word-PHP (section Using native Word formatting with HTML) you can read some samples about how to use MS Word styles when importing HTML contents.
We have moved the request to the dev team to add support for font-size and other rPr styles to checkboxes using HTML/CSS in the next release of phpdocx.