Not sure whether whisking until light and & fluffy entails hand whisking or using a stand mixer. What is the intention here?

The intention is to introduce air into the mixture, since there is no leavening used to do so except the eggs. If you have particularly well developed arms, you can certainly do this using a hand whisk. The recipe is for one single serving, so it would not likely be sufficient batter for an ordinary stand mixer- but a good hand mixer would work quite well. If you have a whisk attachment for it, that's great- but your basic beaters will suffice. You need to get the mixture aerated as well as you can before folding in the chocolate, or your cake will be a very heavy, dense puck. It would be a tasty one, but not quite the lava cake you have in mind.