The minchas chinuch himself lists a few mitzvot similar to eglah arufah, kiddush hachodesh, and semicha that apply only in eretz yisrael. it's surprising he doesn't answer that this mitzvah (chatzotzros) too is similar to the latter. any mitzvah that is tzibbur related applies only in eretz yisrael. thus war, as well as a tannis tzibbur can be only in eretz yisrael, because outside eretz yisrael we have a status of yechidim. eretz yisrael is metzaref the yechidimi into one nation is explained in the zohar - mi keamcha yisrael = goy echad baarets. when are we echad baaeretz.
in conclusion, why doesn't the minchas chinuch understand the mitzva of chatzotzros to be a mitzva which applies only in E"Y?
avrohom adler, usa
The hypothesis you present is interesting. However, I don't think that this is a question on the Minchas Chinuch, but rather on all of the Rishonim and Acharonim that did not simplify the matter in this fashion. The reason they did not agree, is because there is simply no source in the Gemara for such a general rule that "anything Tzibur related applies only in Eretz Yisrael." Accordingly, the Mitzva would seem to apply everywhere. [If the Zohar would state this rule regarding the Chiyuv of Chatzotzros, I would think someone would mention it in a Teshuva. If someone does, I would be interested in knowing the source.]
All the best,
Yaakov Montrose