Edited to add: For extra credit, it might have been worthwhile to apologize to the merchant for failing to prevent a situation which caused their wares to be presented in an unflattering manner.
This probably stands reality on it's head, but what actually happened on one particular day in Tokyo is not maximally relevant to Groupon's Japanese business, and having a reputation for being magnanimous and savvy to how the game is played can only help them in the future. Again, though, I think they did really well.
Bowing in this situation seems like a high-risk, low-reward behavior. He might have moved the apology from an A to an A+, but he also might have made the situation worse without realizing it. If I bowed for an apology, I feel I would make any number of rude mistakes, like maintain (or not maintain?) eye contact, have the wrong facial expression, not bow deep enough / shallow enough, slouch, not hold it long enough, do it sitting, or check Twitter at the bottom. When you don't understand a culture, it's usually reasonable to be polite and gracious within the confines of your own. Maybe Japan has different expectations, but I've worked with an uncountable number of foreign nationals, and it's understandable when they don't extend a handshake (typical American greeting), or yell "Hey, fuck you! How you doin'?" (typical New York greeting).
In this regard, foreigners are a lot like dolphins. You're going to be graded on a curve and that curve is going to underestimate you severely -- one can (judiciously) take advantage of this sort of thing.
My ex-ex-job was Coordinator of International Relations for a tech incubator, and I never saw someone lose points for trying their six word Japanese vocabulary, a bow, etc. It may actually be more difficult for those folks who are in the uncanny valley of between "fluent enough to be assumed competent" and "actually competent." (cough Oh the stories I can't tell. cough)
Tangentially related, it is occasionally to one's advantage as a foreigner to pretend ignorance of Japanese social norms. I am not generally a fan of it, but sometimes duty wins.
You are what you eat, and if you eat what they eat, you are in some sense made of the same stuff.
Humans like to put other humans in two boxes, "us" or "them" and nothing can get you over the threshold and into the "us" box better than eating their food. In my experience, I've also found that most people want people in the "them" box to be in their "us" box and will lightly test your suitability with various social normalization tests -- often in the form of some local delicacy that they know foreigners won't be into. "Here! Try some of this delicious fermented cow stomach!"
(it also helps that most places have a friendly social structure around alcohol consumption, and chasing bites of random animal innards with some hard booze seems to do a good job of killing off whatever might not agree with you)
It also usually follows that they'll see you put a good effort into meeting them (culturally) and most folks will give you a wide berth to stumble through their social customs.
Without knowing anything else about a place, I've managed to muddle through relations with Peruvians, Ecuadorians, French, Russians, Chinese, Koreans, Saudis, Germans and a few others simply by sitting down at a table with them and breaking bread and trying to mind my manners.
In a few places, this immediately broke down walls of outward hostility and the night often ended with some kind of embarrassing duet at a Karaoke bar or similar.
I mean, he is alone in a shirt, no suit, no tie, seamingly from his personnal computer (no pro involved, no one else), with an improvised background.
It may be felt as sincere and straightforward, but on the other hand it lacks seriousness and commitment. One would say he didn't care to do something more formal, or even to get someone to help, and just hacked a quick reply before getting home.
I seems more targeted at future investors than to angry customers.
Edit: perhaps I should add that the apologies from groupon japan on the official site where basic style, plain text ones. This is the first video published on the issue, so it's a bit jarring to see something so casual.
Merchant protection is something that really needs to be done better.
I also liked that it was all done in one take and it wasn't given corporate PR-treatment, it was just a guy in front of his webcam. Also quite clever to do it at the office, when everyone has gone. Gives the impression of the hard-working shacho (which I'm sure he is, anyway).
It came across as a business owner who genuinely cares about customer experience.
There are forms of apology which are distinctively Japanese. One is a videotaped press conference during which a speech very similar to that video would be delivered by the CEO. He would likely be accompanied by three or four people close to the matter. At a scripted moment during the speech (likely, several of them), all will simultaneously bow deeply. On the video you would hear audible clicking noises as every print photographer in the room simultaneously went for the photo opp, because Japanese papers run with photos of bows for apologies the same way American newspapers run with photos of handshakes for peace treaties.
If you're not serious: This joke is in extremely poor taste.
Suggest removing sticks from nether regions... both of you.
Japan has twice the suicide rate which is still not a lot. It's about the same as Finland. This is not a subject that can be (nor should be) easily reduced to a "Japanese people commit suicide a lot" kind of stereotype, so lets not do it.