Volume of the material and volume of the demand for the material, probably.

The foam for the beds is extremely compact when vacuum sealed, and is used in tons of other products.

The standard fabric cover is also probably produced in massive quantities for other products, and also folds down to be quite compact.

Faux fur is basically only used in blankets, pillow and toy linings, and depending on how dense the "fur" is, may add quite a bit more volume (a bigger problem if shipped to the US from a separate supplier than the foam).

With that said, $100 does seem rather steep for the cover. I'm assuming they had to use a specialty version to make it more rugged than the cheaper stuff used for other products to be pet friendly.