That depends on what the rights guaranteed in the Second Amendment are. What was the purpose of the Second Amendment? Was it to make sure every American has the right to own an arsenal? Does that even make sense at a time when the only weapons in existence were swords, bayonets, cannons, and black powder muskets?
In 1791, when the first ten amendments to the Constitution were ratified by the original states, there were no six guns or repeater rifles. These were 30 years or more in the future. There were cannons and muskets, which took from one to five minutes to load. Really!
The photo below shows the kind of weapons used in the 18th Century. It is taken from the website of a company that makes gunpowder for antique rifles.
The Bill of Rights was not directed at individuals. It was to persuade the Colonies to join into a union instead of becoming separate countries. The concern in the Colonies was to keep their separateness and not be taken over by a central government as was already the case with England. They agreed to a Federal Government as long as it was weak and would not take away their individuality.
The Bill of Rights was more of a State's Rights document than for Individual Rights since most residents – women, slaves, Indians, immigrants, renters, tenants, and those without property – had no rights anyway. Ah those "good old days," when wealthy White Men ruled and everyone else was subservient.
The Second Amendment contains two clauses, the second of which may or may not depend on the first but almost certainly does.
A well-regulated Militia, being necessary to the security of a Free State, the right of the people to keep and bear Arms, shall not be infringed."
What that says to me is that states can establish their own Militias, and the members of State Militias have a right to be armed. It doesn't mean all citizens of the union of states have a right to be armed.
Also since we know that the arms available at that time are nowhere near what are available now, the Second Amendment only refers to the primitive arms that existed in 1791. If James Madison, the author of the Bill of Rights, and the representatives from each state that signed it, could have imagined the kind of arms that are available today, they would have certainly put additional restrictions on what individual citizens have a right to own.
So we come back to the question ask at the top. Does Obama's Executive Order violate the Second Amendment? No, because it is still left to the individual states to enforce their interpretation of Militias, but additional Federal supervision is provided. It's a little like sending your 18 year old "adult" to college, but sending a bodyguard along to keep him/her out of trouble.