This headstamp symbol is found in both a single-entry version, and the double-entry version you show. However, I believe the symbols are actually a dot enclosed in parenthesis, rather than enclosed in a full circle. It is my impression, from the few I have seen, that the one with the single “dot in prenthesis” headstamp is scarcer than that with the double-symbol marking. I have no documentation for that opinion, it is, as I said, simply an impression created by what I have personally seen.
I had one of the double-dot headstamped rounds once, but have never had one of those with the single mark, nor have I seen hardly any of those.
The menaing of these marks seems to be unknown. In Ken Elks book, Bolume I, page 62, “Japanese Ammunition 1880-1945,” he theorizes that these could be experimental rounds, with the headstamps marked for that reason, since he describes the differences between these rounds and the normal, unheadstamped versions as “very slight, almost undetectablein a casual inspection.” While I have no idea what they mean, I am not inclined to agree with that, although I certainly could be wrong. While certainly scarce, I am concerned that they are a bit more common than it is likely for any experimental, or even very limited issue rounds, to be. I note, for example, the 7 mm Nambu Dummy round and the 8 mm Nambu red-wood bulleted blank cartridge, both of which were issue cartridges, not experimental, but both of which are perhaps even more uncommon than these headstamped 7.7 mm rounds.
Elks indicates probable manufacture in 1940-42, but shows a box label for experimental rounds dating from “circa 1938” that could be for the ones with these odd headstamps. It is not confirmed as such, however.