Employment excludes non-salaried directors, volunteers, persons paid by commission only, and self employed persons such as consultants and contractors.
The actively trading businesses with zero employees are therefore those businesses where the staff members are drawn exclusively from that group. That may cover most one-person outfits, perhaps some family firms, groups of self-employed people, and so on. These businesses are typically formed in that way as a response to particular regulations, usually tax rules.
The answer is in the explanatory notes attached to that dataset, section 56, from where the above quote is taken. The explanatory notes are attached to that dataset to answer questions such as this. When you have questions about a particular dataset, the explanatory notes (which might also be called metadata, data descriptors, or similar), will usually have the answer, as they do in this case, and should be any enquirer's first place to look.