When one leaves his/her home town traveling without a specific destination until reaching
the distance limit for shortening the prayer (e.g. a shepherd looking for good grazing for
his sheep, a picnicker searching for a more suitable place for camping, or one chasing a
fugitive) is he/she allowed to shorten prayers?

According to the majority (of Muslim scholars) one would not be allowed to shorten prayers, since
the traveler in such a case has set off without the intention beforehand (and the intention is of
significance in Islam). Therefore he/she has not met the condition of being a traveler.