Deal is a description of the material, not the form, of the desk. In this case, softwood such as fir or pine.

The 1848 novel Mary Barton, by Gaskell, uses the word in this way:

Opposite the fire-place was a table, which I should call a Pembroke, only that it was made of deal, and I cannot tell how far such a name may be applied to such humble material.