The Mishna (megillah 23b) there lists a number of things which require 10 men, and includes saying God's name in the zimun for birkas hamazon. The Gemara then goes on to explain the reason for everything on the list: all "Devarim SheBikdusha" require a minyan (based on some verses), and, in the last few instances, (including Zimmun beShem and Birkat Chatanim), the reason is that it isn't appropriate ("אורח ארעא" the way of the land) to say those without a minyan. Thus, the implication appears to be that, while all devarim shebikdusha require a minyan, not all things that require a minyan are a Davar SheBikduasha, and zimun seems to belong in the latter category. This is most likely the Aruch Hashulchan's reading of the Gemara.
However, the Mishnah Berurah (199:15) and Kaf Hachayim (199:20) statee explicitly that Birkas HaZimun is actually a Davar SheBikdusha, based on the Levush, and this appears to be the position of the Kesef Mishnah (Hil. Berachos 5:7) as well.