Bill: Perhaps the original meaning was something like go within a circumscribed area. The go classic, Guanzi Pu, (known in Japan as Kanzufu), has both life and death and yose problems, for instance. But it has come to mean life and death problems. Similarly, tsumeshogi refers to shogi mating problems. Perhaps the shogi term came first, where the king is contained and killed, and came to mean life and death in go by analogy. John Fairbairn would probably know.
JohnF I don't know which came first but, yes, tsume means abbreviated or compressed in this case. It shares the same root as -tsum- in damezumari but even in the case of tsumaru/tsumeru the meaning is one of compressing the space available, packing something in (e.g. canning is kanzume). Kanfuzu is wrong. It should be Kanzufu, but really as it's a Chinese book we should refer to it as Guanzipu (or Guanzi Pu). I put in kanzume as a tease - the kanzu here has nothing to do with kanzufu :) It's the aberrant Japanese reading of guanzi.
Bill: Thanks, John. Kanfuzu corrected. ;-)
hnishy: The Japanese National Diet Library Digital Collection allows you to search words in Tables of Contents of nearly one million old books. The first usage of "tsumeshogi" shown in the data was in 1897, "tsumego" in 1899. Therefore it's almost certain that "tsume-" was borrowed from the corresponding shogi problems; the verb "tsumeru" is the usual word for checkmating in shogi, not used for killing in go. Newspapers and magazines usually publish a tsumego adjacent to a tsumeshogi.
JohnF Hayashi Yutaka cites the term tsumego in a book "Kifu" by a 1-dan pupil of the Inoue family, Okamura Taminosuke, which is dated January, Meiji 20 (1887). (I have not seen it, so I have no idea what the format was). He also cites tsumego in other books predating 1899, and one of these (Igo to Shogi of 1897) even, apparently, discusses tsumego and other aspects of go in comparison with shogi. Again, I haven't seen it. Hayashi makes no comment on the dating of term but elsewhere he does say that tsumemono was the old term for tsumego, and that term is used even today for 'stuffing.' (And an even older term existed - tsukurimono.) Under 'tsumego' itself, however, he does say that it refers to problems given in magazines and supplements, where space may have been at premium. A tsugi no itte whole-board position was the first to appear in a general magazine, supposedly in imitation of the Times chess column, but it seems that tsumego took over rather quickly - space constraints again?
hnishy: If you are interested, the 1897 book "Igo to Shogi" can be viewed in the Digital Collection: https://dl.ndl.go.jp/info:ndljp/pid/861063.
JohnF Thanks for the link. I found it too tedious to scroll through the whole book, but what I did look at was enough to make me believe that Hayashi may have been using the term tsumego as a shorthand (by analogy with tsumeshogi) as I didn't see the term in places I would expect to see it (e.g. the index), whereas tsumeshogi did appear. Furthermore, the way tsumeshogi was used, without any definition but with references to masters of the Ohashi and Ito families of long ago, gave me the impression that the term was expected to be familiar to the reader. However, the author did also use the more general term tsumemono, so questions remain.
Looking at this topic from another angle (one I prefer as a journalist), modern-style newspapers, as opposed to the older yomiuri handbills, appeared in Japan in the Meiji period under western influence. One significant aspect of such newspapers (and magazines) was that they were large format and columns were used for ease of reading. But columns had a major extra justification in newspapers in that they allowed quick editing (e.g. when updating an evening edition from a morning one) and they also allowed easy demarcation of the many short stories on one page.
In the case of chess columns, they therefore had to fit into this columnar design, but for an 8x8 chessboard that was not too much of a problem. It was also not too much of a problem of a problem for 9x9 shogi. It should also be noted that both chess and shogi (where the pieces actually move) also used text coordinates for the answers, so that the use of diagrams could be restricted. But for go, the tradition had long been to use a whole 19x19 board into which several different problems could be inserted, and the answers were typically shown on a subsequent diagram, with no text. The use of text answers was, of course, known as long back as the Wangyou Qingle Ji, and much more recently Hayashi Genbi used it in Japan. But it was never a user-friendly system, and diagrams were nearly always preferred. But when newspapers came along, it seems that a decision was made that go diagrams had to be compressed to fit into the columnar format. It would not be strange if someone felt a term for this new compressed format was required, at least in journalistic circles, and it would be reasonable to take a cue from a pre-existing term, either tsumeshogi or tsumemono. But, as I see it, and this is in line with discussions I have had with Japanese go historians, the use of the 'tsume' portion in go relates to the compressed miniature format, and so could even originally have been a punning journalistic term rather than a go technical term. The timing of the first appearance of the term in the mid to late Meiji would accord with that kind of evolution. The Yubin Hochi began its tsugo itte feature in 1890, and other newspapers could be expected to want to ape it, and one way to be different would be to "invent" a new-format tsumgo.