"Dispatches" means official news reports or directives coming from a news agency or a government bureau. It's a joke because such an official report makes no sense in this context. Here, the dispatches are merely the banter that Ken tells him. Referring his banter as "dispatches" is a stylistic contrivance intended to be clever and humorous.

Dispatches from the front line means a reporter reporting from a war zone, the front line(s). They are analogizing the excitement of his nights out to a war.

Think about "dispatches" as a plural noun. They are saying that nights are dispatches (it might just be a style of writing).