It was likely unintentional here, but that dialect is Middle English; it sounds like "what" to our modern ears (so it's eggcorned into it a bit), but the word is really "wot." As far as I can search, wot is just defined as "know", but it seems to get used in place of "that" fairly often despite that definition, even by Shakespeare, so it's not like it's an unofficial use.

A clear example of the eggcorned form is the title of the fifth chapter of the Poignant Guide: "Them What Make the Rules and Them What Live the Dream."