Thanks to Stack Overflow:
Here’s what’s causing the problem:
The baseline of an ‘inline-block’ is the baseline of its last line box in the normal flow, unless it has either no in-flow line boxes or if its ‘overflow’ property has a computed value other than ‘visible’, in which case the baseline is the bottom margin edge.
Changing .badge-wrapper.box span from overflow: hidden; to overflow: visible; fixes it.
Edit: Setting vertical-align: text-top on the .category-dropdown-menu badge-wrapper.box link accomplishes the same thing, but would allow you to set a max-width on the category name span and have the name truncated with ellipsis. (there’s currently no max-width on the menu’s box-style category span.)