Today, Google Chrome (the world's second largest browser) got all of these APIs and more (except WebRTC, but it's in the dev build, so it will soon be here too). Chrome even have it's own built-in appstore (Chrome Web Store) where users can install extension/apps, without having to restart their browser.
This would be the easiest way for the Spotify developers, as they only had to tweak their code very little to make it compile with NaCl.
( Offtopic: I made a chrome extension for Spotify, which convert spotify links to links with mouseover info, for example image of the album, artist name, title of track, popularity. Get it HERE. Thank you :] )
Now you can try our brand new web player at spotify.com
The web player will be a bonus if you can’t - or don’t want to - download our app. So whether you’re at the office, or round at a friend’s house, simply log in to your account and hit play. You can play the entire Spotify catalogue directly from any supported web browser. Chrome, Firefox, Safari and Internet Explorer are all included. The web player is available to all users, whether you’re Free, Unlimited or Premium.