Rav Shapira responded explaining that the mitzva of lighting the Chanukah menora is in one's house. The concept of lighting the menora in shul is a minhag to accomplish pirsumei nissa, publicizing the miracle, even though there was never a rabbinic decree to light in shul.

Reasons given for this minhag include:

1. for the benefit of guests without a home to light in, similar to the custom of saying kiddush in shul on Friday nights.

2. in the Diaspora it was often dangerous for Jews to light the menora outside their homes properly, this was a way to have a public lighting that would accomplish the publicizing of the miracle

3. as a commemoration of the lighting in the beis hamikdash

4. a bracha is made on the lighting in shul even though it is only a minhag, just as a bracha is said when reciting Hallel on Rosh Chodesh, which is also a minhag

This has become the common custom, to make the rbacha on the lighting in shul, even though it is just a minhag and there is some halachic opposition to it, and even Sefardim make a bracha on the lighting in shul even though they don't make a bracha on Rosh Chodesh Hallel.

A common question is if one should light the menora at any public event, such as Chanukah parties, weddings during Chanukah, and the like, similarly to the way we light in shul, as another opportunity to publicize the miracle. Many poskim have said to not make a bracha at such lights, but some poskim have said that one should make the bracha when the party is taking place outdoors, especially if the people who already lit did so indoors in their houses rather than outdoors.

So the question is if davening in a minyan outdoors is like davening in a shul with the minhag being to light with a bracha or maybe it is like any public gathering in which most poskim hold no bracha is made?

It seems such a minyan could be compared to a shul and they would light with a bracha. Even regarding parties some rabbonim have paskened that if there will be davening at the event it would be considered like a shul and they could light with a bracha.  

In the case of the original question regarding the street minyanim, because the minyanim have already been in place for a long time, it should be considered like a shul, and they could light the menora at the street minyan with a bracha. 

source: Ynet