Personally I'm mostly offended how stale and unoriginal a lot of these jokes are, but I can definitely see why the censors took offense at some of them.
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.