WebApi is not a platform for continuous services. Its purpose is just to provide an interface to your application over HTTP.
In this scenario, WebApi would only be useful in its ability to accept requests. The data in the request can then be used to query your long running internal systems for data, or to update or create new data. WebApi embraces the HTTP verbs (GET, POST etc) for this exact purpose, making HTTP the protocol of your application's state.
Also, with regard to returning data. WebApi simplifies the serialization of a complex object into javascript (by default, overridable if need be). This is useful when your Api is consumed by clients speaking json.