The food at Asian Place is decent. While there are a few restaurants at the Zurich Airport Renaissance Hotel, Asian Place is probably the most suitable for vegans. The menu does not explicitly name any vegan items, but all of the curry dishes and stir fry dishes are made to order and can be done without animal products (just ask your waiter - mine seemed very willing to accommodate my dietary needs). In addition, there are vegetable spring rolls which do not contain any egg.
On Saturday nights, there is an all-you-can-eat sushi bar with some vegetable sushi options. However, the cost (79 Swiss francs) is the same regardless of what you eat, so it probably isn't worthwhile for vegetarians and vegans to consider this option.