You could use Flash to create this, however less and less users would be able to see it. But then again newer versions of Flash lets you export to HTML5 and canvas.
The Splash and bubbles website isn't created that way though. It is a fairly straight forward HTML5 site with each element positioned absolutely with css. Then there is a javascript script running every time you mouseenter (or mouseover) one of the elements which triggers one of the sound clips (which will be played by the browser). On top of that there is some CSS based animations running for the characters and on hover.
Basically this page is a mix of html, css and javascript. If you want to make something similar you should learn html, css and JS/jQuery or find a frontender which can help you implement it.