That's not quite how I understood it

> Do the cutout in feature space, not the original input space.

I think they do the cutout in the original input space, based on examples they show, e.g. they mask parts of text and grey out parts of an image.

> and make the network predict the missing part

I think predict the latent representation (as you say in (2)), but not of the missing part, but of the whole corrupted sample, and require it to be close to latent representation of the original input done by the teacher.