Ostensibly, Chrome is a web browser. More than that though, it's a platform, especially in Chrome OS form. While using web technologies, apps for Chrome aren't the same as an app built for the web. Now, Google is moving further in that direction with the Sync FileSystem API.
The Sync FileSystem API is yet another HTML5 API that allows developers to use local storage and enables apps to work offline. There are several options for doing that already, what the Sync API brings new is, as the name suggests, the sync features.
Specifically, while the data is stored locally, it's also synced to the cloud, making it available to copies of the same app running on different devices and in different browsers. For now, the API only works with Google Drive.
This should make it possible to pick up your work where you left off even if you're using a local web app. The feature is available in Chrome 27 Canary, which means it should make its way into the dev channel as soon as Chrome 26 graduates to beta.