Shabaik's conviction was predicated off the fact that he and his cohorts attempted to prevent Ambassador Oren from speaking at a lawfully constituted assembly. Shabaik half-heartedly tries to downplay this goal, but mostly owns up to it. His argument against the conviction centers mostly on the grounds that this form of disruption is the only effective way the protesters had of communicating their message.
[Q]uestions and answers are not an effective form of protest against states, especially those engaged in war crimes and possible crimes against humanity. States enhance their power by creating a framework within which non-state players can challenge state policies. Due to an imbalance of power, to effect real change ordinary citizens must challenge state power outside of this framework. We did not wish to politely ask questions but rather to make a poignant statement. We came to protest Israel’s actions, and a Q & A session was not the means through which we wanted to act. An effective protest must voice its opposition in a manner that challenges the policies Oren represents and the framework through which those policies are propagated.
Let's break this down a little. States entrench their power by "creating a framework within which non-state players can challenge state policies" (here presented in the devilish form of a question & answer session). These frameworks -- for simplicity's sake, let's call them "time, place, and manner" restrictions -- must be broken out of in order for citizen's voices to have a real effect. Hence, the speech had to be disrupted.
One perhaps notices right away that this is not particularly well-argued. Whether or not ordinary citizens can challenge state power from within or without the framework's the state sets up for hearing dissenting views would seem to depend on the structure of the framework itself. Even if the "poignant message" the protesters wished to send was not one that could be expressed through Q&A (say, "Ambassador Oren is representative of an evil so grave one cannot and should not converse with it rationally"), it's not clear why that message could not have been delivered via, say, picketing. I'm dubious that the expressive message of the protesters could not be put forward in a way that was non-disruptive of the speech.
But perhaps the claim is deeper -- Shabaik is making some sort of Nietzschian argument about the need to break free of state bondage, regardless of the content of the chains. This might or might not resolve another tension in Shabaik's argument (whether the "framework" being protested here is American -- since we're operating under American law after all -- or Israeli), but it does perhaps explain why disruption was "necessary" to fulfill the expressive needs of the protesters.
The problem here is that -- if the goal is to lash out against state-imposed rules regarding speech -- it is unclear why they expect the state to play ball. They want all the glory of rebelling against the state, but then they get all aggrieved that the state might not react kindly to it. They bite one hand of the state while expected to be shielded by the other. It's like Gollum -- "The state is our friend/We hates the state!" -- and more than a little weird.
Now, this is in a sense beating around the bush: the protesters had more than just expressive desires but substantive ones as well, one of which was to prevent Ambassador Oren from delivering his speech in a public forum. Contrary to Shabaik's assertion, this is something the government (and First Amendment values) can and should care quite a bit about. Indeed, while Shabaik blithely asserts that "rights can only be trampled upon and censored by the government, not by individuals", nobody actually believes that. While most constitutional entitlements are only enforceable against the government, most of what government does is to try and protect various rights and entitlements of the citizenry against private encroachment. We have the right not to be murdered, and so the state provides police. We have a right to be able to make the case for our preferred policy positions in the public forum, and so the state provides rules by which that debate can take place in a fair and open manner. And this is reflected in the law that Shabaik violated.*
One rationale behind "time, place, and manner" restrictions is that they give the state the tools to ensure all sides of hotly-contested issues have the opportunity to state their case and be heard. While we are willing to allow tremendous diversity in how any person elects to state their case, one thing we don't generally stand for is for them to forgo that role entirely in favor of simply trying to drown out the other. Shabaik quite wrongly argues that the First Amendment instead is some sort of codification of The Wretched of the Earth wherein those "without power" are given free reign to determine which voices can be heard and which ought be silenced. The First Amendment most certainly does not instantiate that principle. Its mantra is for "more speech, not enforced silence."
* It is worth admitting just how much of an embarrassment Arizona Free Enterprise Club v. Bennett is to this line of argument.