in the video she creams the butter & sugar with a stand mixer. in the directions it says stir with spoon or spatula. seems like a big difference

I’ve made this cake both ways … it’s infallible and one of my all time favorite cakes !

You can make this cake either way.

As a child, I made cakes creaming softened butter and sugar for several years before my mother allowed me to use her hand mixer. Especially for a somewhat rustic cake like this, creaming with a spoon is perfectly adequate. I'm guessing that the person in the video just prefers to use a mixer, as it seems easier.

The batter beaten with the mixer may produce a finer, somewhat lighter crumb. Ultimately however, the cake will be delicious, either way. ;o)

It's not a big difference. The stand mixer does with a motor what humans have done for millennia with their hands.

I don't own a stand mixer so all of my baked goods come from a wood spoon, spatula or whisk just like someone a hundred years ago would have baked.

The discrepancy is because the person in the video (Amanda Hesser of Food52) and the recipe author are two different people.

In any case this confirms that this recipe can be easily executed by hand or by machine. It's entirely your call which method you decide to use.