Keep in mind that Shakespeare wrote a number of Sonnets, so he is regarded also as a poet in addition to a playwright, which puts in squarely in the category of

Keep in mind that Shakespeare wrote a number of Sonnets, so he is regarded also as a poet in addition to a playwright, which puts in squarely in the category of "writer". Since his plays were written in verse, with very little in the way of stage direction, less in props, and next to nothing in scene descriptions, it's not too far of the mark to think of the plays as poems themselves. When people read, they hear 'silent prosody', or a spoken voice, in their heads, so even when reading, they are hearing the words.