Neither is correct. In your first statement, you have two examples. In the second, you have two examples from two different groups. They should say:
- Sushi and Tempura are examples of Japanese food.
- Sushi and Peking duck are examples of Japanese and Chinese foods, respectively.
An exception to this would be if the name of a dish combined two items, for example, "rice and peas is an example of Jamaican food".
You'll notice that, in example 1, I have made 'food' singular. When speaking about a specific cuisine as a whole, we normally use the singular. However, in example 2, it is correct to use the plural because you are speaking about 2 different kinds of food.