Projects have success metrics, and a lot of these metrics are based on customer interactions. These metrics may include something tangible like the amount of sales of a product, adoption and usage rates, or something a little less tangible like increased efficiency.
These should be defined at the very beginning of a project, and sometimes can morph during the lifespan of the project, but will always involve some version of customer happiness. Happy users are just the same as happy customers.
In thinking of users as customers, more time will spent ensuring project success by making them happy. More time will be spent figuring out what pains them currently and where improvements can be made. More time will be spent talking to them before the project begins and helping to ensure their happiness.
Projects need money to build and enhance. Without customers, funding runs dry and energy and attention are paid to the shiny new thing. Keeping customers happy and engaged are the primary ways to ensure that a project is successful and keeps the money flowing in.
So lets extend the traditional meaning of customer to include all the users of a web application, no matter what type of application it is. Users are now customers. Go make them happy.