The gemara quotes a machlokes whether reading megillah requires a minyan. Rav holds b'zmana (on 14 or 15) it does not, shelo b'zmana it does; Rav Asi disagrees and says it always requires a minyan. Rashi explains the purpose of the minyan here is for pirsumei nisa. The gemara concludes that Rav was choshesh for Rav Asi's opinion and gathered a minyan even when he read b'zmana.
Based on a statement of R' Yochanan in the next perek that mentions reading b'yachid, Tosfos paskens l'halacha that m'ikkar hadin Rav's chiluk is correct - a minyan is not required m'ikkar hadin for the reading b'zmana. The Ba'al haMaor, however disagrees. Ba'al haMaor understands that the whole machlokes Rav and Rav Asi was only l'chatchila what the optimum practice should be; however, b'dieved (as R' Yochanan's statement reflects) everyone agrees reading without a minyan is permitted if not minyan is available. The Ba'al haMaor cites proof to his position from the Mishna that lists mitzvos that must be done b'tzibbur, and kerias hamegillah is not on the list!
According to Tosfos, how do you explain this Mishna? The Ramban answers that there is a difference between mitzvos that must be done b'tzibur and mitzvos that are a chovas hatzibbur. Keri'as hamegillah is a chiyuv on each yachid, but which (according to Rav Asi) should be performed in the public setting of a minyan. The mitzvos listed in the Mishna are chovos on the tzibur as a whole, not each individual. (See Chaim Markowitz's discussion of keri'as hatorah, which is subject to the same machlokes http://nefeshchaim.blogspot.com/2006/02/parsha-chabura-beshalachthe-obligation.html).
Based on Rashi, perhaps one could also distinguish between two different halachos with respect to the idea of minyan. By the cases of the Mishna, the requirement of 10 is part of the formal definition of tzibur inherent in those mitzvos as divrei kedusha. By megilla, the keri'ah per se is not mechayav minyan as a dvara sheb'kedusha, but rather the din of pirsumei nisa requires a public recognition of the nes.