In the score of his madrigal Ah, dolente partita! it says "Lento, ma in due". Lento means slow, right? But what exactly is it that is to be divided in two?
A literal translation into English is probably best: "Slowly, but in two." "In two" means that there should be two beats per measure.
This affects not only the tempo, but also the phrasing and the rhythmic organization of the meter. Try listening to the video you linked to twice, once tapping along in quarter notes, and once in half notes. I think you'll see the difference even though the actual tempo is of course the same.
Also, I noticed that the tempo indication is in parentheses. Does this signify an editorial addition or not?
Yes, as noted by guest in another answer, it is an editorial addition. The score in the video is from Gian Francesco Malipiero's edition of Monteverdi's complete works. The volume containing the fourth book of five-voice madrigals was published in 1927, which is I guess around the beginning of the period in which editors started to be careful to identify their contributions. The original was published in 1603.
Since guest has added a link for a PDF copy of the original part books, I won't include that, but I will encourage you to print the parts and try singing from them. It's a remarkably edifying experience.