It seems that beyond the "to snatch" concept (
arranque) it had a figurative meaning of "an instant". Maybe because the original word meant a sudden and quick grasp, a violent action (as the words
It seems that from there it came to be used as "a period of time a little bit larger that an instant".
-Rato, del latín 'Raptus': en su origen significaba ‘tirón, arranque’ y, figuradamente, ‘instante’, acepción esta última que viajó a América, al mismo tiempo que en España tomó el sentido de "un espacio de tiempo algo mayor que el de un instante"
I found this explanation (in Spanish) here (actually it also explains the origin of
broma, in relation to this other question and other words whose original meaning has nothing or not much to do with the actual meaning. I think you might find that reference interesting, given your latest questions about etymologies. If you need further clarifications with the content of that site just tell me and I will edit the answer to enhance the explanation).