There are tons of different kinds of chinese food that will appeal to different people- take for example szechuan food. Her solution to stereotype a culture is nothing new, but she could have done her research and not have been so insensitive.
I'm going to bring up Kwame Appiah again as an illustration of this exact point.
In his newest book about identity he touches on cultural appropriation briefly, mainly to celebrate it. After all, it's how most any "authentic" cuisine we have was formed - Brazilian cuisine, for instance, is a mixture of Latin, African, Asian, and European cuisines to form a coherent new style of food. Or, in a more salient example, we can look to how rap has proliferated across the globe to become an artform of rebellion and social causes, emanating from a few blocks in New York, and itself built on African musical styles and spoken word, to cross the globe and be used by many who saw its anti-power tendencies and how that could translate to their own oppressed groups.
What Appiah points out is that what we think of as negative in appropriation is not appropriation itself, but lack of respect. Which goes to your point about insensitivity.
A pun can be just a pun. Iconography can be simply images. They can be used respectfully, or not. And this place doesn't, on a surface level, appear to respect the culture it is working within. There were hundreds of ways for this restaurant to respect the culture, either Chinese or Chinese-American, it dabbles in, but instead seems to think it can do better than them. When, given the subjectivity of food, better is a fraught term.
