I don't believe in the truth of either statement — that he hasn't had a cigarette in about 6 years and that he's scared of his wife — but I don't hear an intent that these remarks be taken as true. I hear an off-the-record interaction with one individual that's about making a friendly connection. There's camaraderie in displaying that he knows something personal about the other man and — since what he knows is that the man has a substance addiction problem — referring to his own parallel weakness.
He doesn't scold or put down the other man, but expresses hope — hope! — that the man has quit smoking and makes the possibly untrue assertion that he hasn't smoked one cigarette in "probably 6 years." This is an encouraging remark, and I think that it was offered in the spirit of encouragement but that Obama also realized that it might sound braggadocious, so he toned it down with the self-deprecating humor about being scared of his wife.
That gives an explanation for not smoking and works as posing that he's an ordinary guy tending to the demands of his wife, even though he is the most powerful man in the world. This is humanizing and a bit silly, and it's a male-bonding moment, containing the implication that wives are demanding and require appeasement.
If you want to mock or criticize Obama here, I think the more sophisticated speculation not that he's revealed he's subservient and pusillanimous, but that this is misogyny or male chauvinism. Obama is using his wife — both as a stereotypical woman and as the caricature of her that we see in the media — to make points with another man. Michelle Obama is not there. It's a remark about her behind her back. She's not named, but called "my wife." And she's scary. He's not actually scared, just tapping an old sexist mindset that makes it possible to laugh at stupid cartoons like this:
And Obama is simultaneously appropriating the anti-Michelle propaganda of his political opponents. He's casually gesturing at the huge pile of mean-spirited scribblings about how she's always nagging everybody about health, all the miscellaneous things scribbled on web pages and illustrated with photos like this:
Feminists and traditionalists alike can chide the man who engages in loose, humorous talk about his wife behind her back.
"Honor your marriage; keep it pure by remaining true to your wife in every way."