The gemara in Brachos (20) raises the question of whether women are obligated in birchas hamazon or not. It's not a mitzvas aseh she'hazman gerama, so why should they not be obligated? Rashi explains that when you say birchas ha'mazon you thank Hashem for Eretz Yisrael, and since women did not receive a portion in Eretz Yisrael, they are therefore exempt. Tos. does not like that sevara because kohanim also do not receive a portion in Eretz Yisrael, and yet we don't find that they are exempt from reciting birchas hamazon. Tos suggests that women are not obligated for a different reason. Since in birchas hamazon we thank Hashem for bris milah and for Torah and women are not obligated in either of these mitzvos, they therefore are exempt. (The meforshim talk about what about the other brachos of birchas hamazon besides "nodeh lecha..." that do not mention bris or Torah).
In defense of Rashi, achronim point out that the kohanim and leviim had the arei ha'leviim, so they did have a portion in the land. Obviously Tos was not moved by that consideration, and the question is why not.
It could be the shoresh of the machlokes here is what we mean by getting a portion of land. Rashi acknowledges that there were women who did in fact receive a cheilek in Eretz Yisrael, e.g. Bnos Tzelafchad, but he explains that they did not receive that cheilek as a nachala the way men did, but rather as a yerusha from a parent. When it comes to the arei haleviim, do we look at these cities as the nachala of sheivet levi, or perhaps they are really the nachala of the other shevatim, just those shevatim have a mitzvah to surrender some of their portion to the leviim to live in in exchange for the leviim and kohanim's service in the mikdash?
The Minchas Chinuch has a different safeik that I think may hinge on this same point. Kohanim and leviim do not receive a portion of land in Eretz Yisrael because they are supposed to devote themselves to working in the mikdash instead of farming. They receive terumos and maasros, as we read in our parsha, for the same reason. Rambam (Hil Shemita ch 13) has a chiddush din that kohanim and leviim can receive a portion in future lands conquered by a king that expand the boundaries of Eretz Yisrael, but Rambam holds (see Raavad) that the mitzvah of teru"m still applies in that territory. Minchas Chinuch (408:1) wonders whether the same applies to arei leviim: will the leviim receive additional cities designated as arei leviim in these future territories, or not? I would say that if arei leviim are the nachala of leviim, just like Reuvain and Shimon and every other sheivet gets a nachala, then in those future territories where the leviim are getting a regular portion of land like everyone else anyway, there is no need for the special nachala of arei leviim. But if arei leviim are really the nachala of the other shevatim, just there is a mitzvah upon the shevatim to surrender part of their portion to the leviim in exchange for their work in the mikdash, then perhaps that mitzvah applies irrespective of whether the leviim get their own portion of land or not.