The “nudge” referenced here is just a slight initial imbalance to break the symmetry. This is exactly analogous to a coin sitting unstably on edge, so that the slightest nudge from the wind will topple it entirely to heads or tails. Their point is that , in many scenarios, racemic mixtures are unstable and will “topple” to one enantiomer, just like a coin flip. In a metabolic network, this has a domino effect, causing other molecules to be homochiral too. Once we arrive at biological catalysts, homochiral catalysis becomes self propagating.
This general mechanism solves the conceptual problem entirely but leaves many of the details as open questions. Essentially we know that homochirality perse is not an insurmountable problem. If abiogensis were true and we knew the precursor molecules, we know the experiments we could to to settle precisely how homochirality would arise from them by purely natural means. Of course, not knowing these precursors yet (a separate problem all together) there is a limit to how far we can go.
Nonetheless, from a conceptual point of view, it does not appear homochirality is difficult to account for in abiogensis.