If you go to the DC gun case site
http://www.dcguncase.com/blog/ and look at the finding document, the finding is the first three pages. Everything after that is informational, analysis, background and theorizing and not binding.
The section below to answer your question and why open carry is NOT protected
2. Like most rights, the Second Amendment right is not unlimited.
It is not a right to keep and carry any weapon whatsoever in any
manner whatsoever and for whatever purpose: For example, con-
cealed weapons prohibitions have been upheld under the Amendment
or state analogues. The Court’s opinion should not be taken to cast
doubt on longstanding prohibitions on the possession of firearms by
felons and the mentally ill, or laws forbidding the carrying of fire-
arms in sensitive places such as schools and government buildings, or
laws imposing conditions and qualifications on the commercial sale of
arms. Miller’s holding that the sorts of weapons protected are those
“in common use at the time” finds support in the historical tradition
of prohibiting the carrying of dangerous and unusual weapons.
Pp. 54–56.
The case was solely about the wholesale banning of an entire class of firearms in common use and the mandatory storage requirement for a limited self rule federal enclave (DC).
The result included what could legitimately be called "judicial activism" as it also added, unasked, a ruling that finally rammed a stake in the heart of RKBA only in the context of "militia" usage.
The case did not ask and so could not place before the SC issues such as but not exclusively
Incorporation of 2A against the states
2A in the context of 9th and 14th amendment ruling
Level of scrutiny appropriate to 2A
What is "reasonable regulation"
What is NOT a weapon in "Common usage" and how is it defined (outside of handguns)
Are restrictions on non functional grounds (magazine capacity, barrel length, bayonet lug, pistol grip etc) inherently unconstitutional
This is why the current Chicago and California suits are so important as they both build upon the ruling as well as create case law.