Designer 2 has introduced the concept of a "working directory".
Each project has its own directory that it owns and will create the necessary files for it to run. Given you put this directory on in a web accessible location (C:\Inetpub\wwwroot\ or ~/Sites/ or wherever your web server is serving from), you will be able to load the designer.html file via http.
Designer 2 also includes a deploy feature much like Designer 1 did. Clicking Deploy on the top toolbar will copy all necessary files from your working directory into a target directory called a deploy path. To configure your deploy path. Open up Settings and it is the bottom option "Deploy Path".
I suggest putting your project directories in a web accessible location so that you don't have to constantly deploy your app in order to run it in a browser.
A 'run' option would be useful. Opening the app using the file protocol is going to be too restrictive so maybe, in the future, it will possible to create plug-ins. For example it would not be difficult to create a plug-in which saves the application and either:
Starts or activates an existing browser instance and refreshes the page; or
Initializes and starts a light-weight web browser such as nginx to serve the application (based on app settings) in much the same way as happens in Visual Studio or Eclipse.
With a plugin framework in place, maybe this type of functionality could be created by users.