The gemara has a question whether the rabbinic prohibition of telling a goy to do an issur and/or benefiting from an issur done by a goy (which the gemara equates by citing the sirus case as a proof), applies only to shabbos since it is more severe (and also yom tov as tosafos points out because shabbos and yom tov are connected), or does it apply to other issurim as well. The maskana isn't clear from the gemara, but the nimukei yosef points out that since all the amoraim held that the sirus case was assur and they certainly don't all hold like r' chidka who says that sirus is assur for a goy, the halacha is that amira l'nachri is in fact assur by all issurim.
Rashi and Tosafos argue whether the gemara is speaking of a case where the jew tells the goy to thresh the grains of the jew or the goy. Rashi understands that the entire discussion in the gemara is where the jew tells the goy to do it for the goy's benefit, something the jew gets no benefit from. This would imply that if the jew tells the goy to do it for the jews benefit, it would surely be assur. According to Rashi the gemara would be making a slight jump by equating the amira l'nachri by muzzling to the interest that the jew has in benefiting from the goy doing sirus (even without the jew saying anything). Tosafos disagrees with rashi and says that it would be permitted for the jew to tell a goy to do it for the goy's benefit. It is only assur for the jew to tell the goy since the jew will be benefiting. According to this approach there is a clearer connection between the case of amira l'nachri by muzzling and the benefit the jew gets by sirus, since even the case of amira l'nachri is for the jew's benefit.
Tosafos assumes that all would agree that it is permitted to tell a goy to eat something not kosher. Tosafos asks that according to Rashi that a jew may not tell a goy to thresh the goy's produce with a muzzled animal, why is it permitted to tell a goy to eat non-kosher? Tosafos explains that the jew telling the goy to do it is tantamount to the jew doing that action. Therefore, telling the goy to eat neveila is like the jew doing the action of feeding the goy neveila which is perfeclty permissible. But to tell the goy to do melacha on shabbos or to thresh with a muzzled animal is tantamount to the jew doing that action which is assur.
R' Yosef Engel (lekach tov 1:8) uses this tosafos to prove the ketzos hachoshen who says that shlichus doesn't work by mitzvos because when reuven is a shliach of shimon and puts on tefillin for him, we don't view it as if tefillin is being put on shimon's arm, rather it is like shimon is doing the action of wrapping tefillin on reuven's arm. This is exactly the sevara of Tosafos. Tosafos holds that amira l'nachri is assur because we are machmir to consider the goy to be the shliach of the jew and therefore the action is attributed to the jew. But, when the jew tells the goy to eat neveila, it is not as if the jew ate neveila, rather it is as if he fed neveila to the goy.
The Nimukei Yosef answers tosafos question by making a distinction whether the goy is using the jew's object or his own object. It would be permitted to tell a goy to eat his own treif food, but not to tell him to eat your treif food. According to the nimukei yosef the issur of amira l'nachri is because the jew has involvement with the action of issur being done by the goy. If the jew has not involvement because his object is not being used and he is not benefiting, it is permitted.