Nice job! The YouTube link seems to be private however, maybe need to make it public somehow.
Just looking at the images, I think the former one looks more organised but perhaps less intuitive whereas the latter one looks easier to grasp but perhaps less visually appealing.
To throw out one more alternative, not sure whether it's neither worse nor better:
Still thinking the first one, let's call it "A" to be the more clear one.
Maybe the boxes are starting to clutter up the view? We could make them smaller, similar to a bullet list, and scale them back up when hovering.
Alternatively, we could have a look at adding some change in appearance when hovering an item. In that way, the checkbox could appear highlighted when hovering an item, and when hovering the family (or "section" as it's called) all related items could be highlighted?