Folks who have Chromecast devices know well that there are two types of casting from the desktop. First there are those applications or sites that support Chromecast directly. This includes services like YouTube or Netflix where the cast button can be found in the video player area and allow you to use the Chromecast as intended, with the content delivered directly to the Chromecast. The other type are those sites that require the user to just cast the entire web page from their browser tab. This is rather slow and requires the content to be delivered from the computer to the Chromecast. Surprisingly, Google did not include the first type of casting for Play Movies and Play Music from the web when using a laptop or desktop. That oversight has now changed.
According to Google, if the Google Cast extension is installed for your browser, you can look for the cast button in the video player area when you fire up your favorite title. This will then cause the movie, TV show, or song to be streamed directly to the Chromecast, just as it would if you had launched the title using a smartphone or tablet.
source: +Google Play