I haven't seen a Chinese person bark. I guess the saying "You are what you eat" isn't true.
That is a very rude joke to make.
I have a lot of chinese friends, I'm trying to be humorous. There is no racist intention.
There have been very few instances of Asian people ever eating dogs, this is really more of an urban legend. Stereotyping an entire race of people based on a sick rumor is offensive to all of them, and you shouldn't be treating your Chinese friends like that, or using their existence as an excuse. If you wouldn't want them to talk that way about you, you shouldn't do the same to them.
It's just a joke. Calm yourself.
Even as a joke, it's not appropriate to say something like that. Racist jokes are offensive and perpetuate stereotypes about people. Instead of telling jokes that are at the expense of others, you should tell family friendly jokes that everyone can enjoy.