For example, the joke about the Chinese restaurant ("I'd be more concerned about what they're passing off as chicken") plays off of the stereotype that Chinese people eat dogs and cats, and the “passing off” remark implies that the Chinese restaurant owners are deceptive and would immorally and illegally serve their guests a different kind of meat than advertised. I can definitely see how that joke would be considered offensive.
The author labels that joke as "harmless" but you don't have to be a Chinese censor to interpret it as reinforcing harmful stereotypes. I dare you to show that scene at a liberal college and notice how few laughs you get.
Similarly, the racist remarks about Chinese people made by Sheldon's mom are somewhat offensive if taken at face value. I guess the joke is supposed to be at her expense instead ("old people are racists" is an American comedy cliche, if a somewhat tired one) but it's conceivable that either the censors didn't get that, or they feared that their audience didn't get that, so they decided to cut it out entirely.
"They wouldn't get that" is probably also the right explanation for censoring the joke about Jews eating at Chinese restaurants during Christmas, which is a very American tradition. That doesn't imply the joke needs to go, but I can see how that would, at best, leave Chinese viewers scratching their heads.
Did you see the recent video where the white guy dressed up in a poncho, big hat, and fake mustache and carried around maracas? He asked a bunch of white kids on a college campus if they thought his outfit was offensive to Mexicans, and they all said yes.
Then he went to the Mexican part of town and asked actual Mexicans, and they all said it was funny or that they liked that he was trying to honor their culture. Not one of them was offended.
So perhaps it would be good to ask a Chinese person if this joke offends them.
Tell me, when Jimmy Kimmels producers go out on Hollywood Boulevard and find that not even one person can point to a country other than America on map (https://youtu.be/kRh1zXFKC_o) - do you think that’s real too? Or is that selectively edited for laughs?
And it's funny you ask about Kimmel, because I actually know the person who did those bits (she was the offscreen voice for the first few years and is actually the interviewer in this video). She said that while it was edited, they didn't have to edit it much, because about 80% of the people really were that dumb.