Some people, of course, were offended. If you look over his history of tweets and the stuff he's written for Family Guy, it's a pretty safe bet that people are offended by his stuff all the time. The criticism of this tweet can't just be that it's the "most" offensive thing he's written, because who cares if it's his most offensive work? Think about it: do we make a big deal when anyone does something worse than anything they've ever done before? No. We only care when people do things worse than anyone has done before.
So is this the most offensive joke every told? The most offensive tweet ever tweeted? No. Is it the earliest joke about Japan that got this much attention? Yes. And that reaction—whether you defend it or dismiss† it—is the doing of the people who were offended. Offended by this joke being too early. And probably more specifically, offended that Sulkin said he was willing to laugh in their temple. The temple of feeling bad.
Some of Sulkin's critics have been calm, and tried to analyze humor. Like this thought from The Comedy Bureau:
Lesson: don’t make jokes in the “never too early” spirit of trying to be as controversial as possible just for the sake of being as controversial as possible, thinking the shock itself is what’s funny. Make jokes because the accepted inconsistency or overlooked false assumption is legitimately funny.
Decent advice, but unnecessary if you're OK with offending people. And sure, the shock is part of what's funny, but that's not the only way Sulkin's joke works.
Some responses have been less analytical and have just tried to express judgement. Like this contribution from from Kasey Anderson:
Always good when stuff like this weeds out the assholes of the world.
Using Anderson's comment as a springboard, Danforth France mixes some analysis with some judgement:
It fails as a joke because it doesn’t say anything true. It makes no point. It shines a light on nothing. If it’s meant to be taken humorously, it reveals a basic ignorance of the subject he’s joking about and THAT is offensive all by itself.
France makes some key claims that—for me—explain the difference in our reactions. He doesn't believe Sulkin said anything true. I disagree. I don't want to get too heavy into an analysis of the nature and structure of humor, but I do see that Sulkin's quote makes a statement about national memory, the history of nations, the nature of pity, the sins of the father, and the size of the world. Yes. Seriously. I'm not saying whether or not he thought all that, but at the very least his instinctual comic ear was picking up those tones.

Let's back up and repeat: It's ridiculous to believe that Sulkin is really claiming that this tragedy is payback for Pearl Harbor, or that the number of people killed in the attack 70 years ago is actually a mitigation on the toll of the earthquake. France is putting a lot of energy into making a point that nobody has actually disputed, unless you take the joke as a straightforward claim, meant to be taken seriously.†
He claims not to be interested in a discussion of "offensiveness or sensitivity or free speech or comedy theory," and he says he disregards the humor simply because "it’s a piece of shit joke." That's disingenuous. Is he out there calling out every joke he thinks is poorly written? It's no coincidence that the joke he's judging most harshly is also being called offensive.† And his very next post he claims a position of "Moral rectitude." He clearly believes this is more than just about the quality of a joke. Unless he believes the quality of a joke is a moral issue.†
Nobody has brought up the issue of harm done by Sulkin's joke, because nobody would be stupid enough to claim there is any. This isn't an issue that society is struggling with more urgently than all other evils. There's no current campaign of bigotry directed at the Japanese that this humor is making worse. There's no tinderbox of Japanese relations that inflammatory speech might set ablaze. There's no risk that jokes like this will make people afraid to help. There's really no risk.
Sulkin has made jokes about child abduction, D-Day, AIDS, rape, rape, incest (of the rape kind)… And people have laughed at them like they're meant to. The only stance that can claim this is now a moral issue, or that this simple joke is more contemptible than any other joke Sulkin has made, is one born almost entirely of the audience's demand that he not make light of their current emotional state. That's a fair (if silly) request. But it's no basis for a claim about his character or humor that you were never driven to make before.
Update:
Sulkin has apologized for the tweet and deleted it from his timeline, posting
Yesterday death toll = 200. Today = 10 thousand. I am sorry for my insensitive tweet. It's gone.
†I have done some minor editing of this post to make some claims more precise and specific. The emended passages are marked.