Strictly speaking, user experience design does not require empathy, but it’s a huge practical advantage. I like getting definitions on the table first to make sure we’re all talking about the same thing. Both UX and Empathy can be broad words.

Empathy: the ability to understand and share the feelings of another.
User Experience: the overall experience of a person using a product such as a website or computer application, especially in terms of how easy or pleasing it is to use.

The overall experience is composed of an analytical task a user performs and also their emotional reaction to it. Don Norman has a good heuristic for breaking down emotional design into:

• Visceral: A user’s immediate, instinctual reaction to the product.
• Behavioral: How does the product feel when we play with it? Do we still like the way it looks? How easy is the product to use?
• Reflective: How you make someone feel when they think back to their long-term usage of your product.

All levels of these are feelings and designing the user experience is precisely about predicting and altering emotions at each of these levels. In theory you can follow design patterns that are known to have certain emotional reactions, but empathizing how a person who is dealing with something sad will immediately inform you to:

• Use solemn, muted colors.
• Not introduce too much optionality into decision making.
• Reinforce a sense of community, etc.

These apply to any product you build for this audience irrespective of audience.

If you can empathize with an audience who is feeling joyful, you would:

• Use lively colors.
• Offer lots of optionality/activities.
• Offer elements of joy, etc.

If you had to really dry it down with a cynical viewpoint, think of empathy as another tool in the belt to pattern match to your audience more effectively.