I don't think so. The pervasiveness of web apps and applications consuming web services means there's a lot of work involving web APIs. This doesn't mean the definition of API was narrowed. It's all about context. If your bread and butter is developing web services, you don't waste time with context-free definitions of your API. You talk about the API and everyone is on the same page.
You even admitted "The pervasiveness of web apps and applications consuming web services means there's a lot of work involving web APIs" and "If your bread and butter is developing web services, you don't waste time with context-free definitions of your API" which is acknowledging the common use definition of API has morphed into Web API. It's only in the context of technical documents or documents that are explicitly referring to non-web APIs that use API and it is understood to mean something other than a web API.