The gemara questions what is the case where a zaken or choleh appoints someone else to do the avoda and eat the korbanos for him. If he is unable to do the avodah and eat, how can he appoint a shliach. The gemara concludes that he is able to do avoda and eat b'dochek, therefore avoda b'dochek which qualifies as avoda he can appoint a shliach for, but eating b'dochek which qualifies as over eating which is assur by kodshim he can't appoint a shliach for. The gemara seems to assume that the kohen who belongs to the mishmar must appoint a shliach to eat kodshim for him. The maharatz chiyus associates this with the gemara in nazir 12a that says that one must be able to do something himself in order to have the authority to appoint a shliach to do it for him. Based on this the Maharatz chiyus asks, the mitzvah of eating kodshim is not a mitzvah on the "gavra" rather it is a mitzvah that the "cheftzah" must be consumed (the chasam sofer and beis halevi discuss this issue in contrast to korban pesach). This is clear even from the gemara's assumption that the elderly kohen of the mishmar can appoint another kohen as his shliach to eat the kodshim for him, which certainly cannot be done by the mitzvah to eat matza because this mitzvah is not an obligation on the individual. But since it is just a mitzvah on the cheftzah that kodshim should be eaten, why is shlichus necessary to allow another kohen to eat from the korban?
It seems to me that this sugya is not at all connected to the inyan of shlichus. The term shlichus over here doesn't refer to the concept of appointing another kohen to stand in his place, rather it refers to the ownership of the rights to eat and the ability to pass on those rights to someone else. The gemara is not using the rule of nazir 12a that one must be able to do it himself in order to appoint a shliach, it is instead using the obvious rationale that one cannot gift to someone else something that he doesn't own. The ownership of the mishmar in kodshim is only when the individual is able to participate in that activity, whether it is avoda or eating, in which case he can offer those rights to someone else. But when he is unable to do avoda or eat, he is not considered someone who has ba'alus over that activity and therefore cannot pass it on to anyone else. Therefore, the gemara concludes that the case must be that he can do avoda b'dochek, so he can gift that right to a friend who is a kohen and not in that mishmar, but since his eating b'dochek would not make him eligible to eat kodshim, he doesn't own that right and cannot pass it on.