Flash is driven by ActionScript which is a language that reads quite a bit like JavaScript. The reason why it works for anyone is b/c they have the interpreter downloaded to their computer (and usually plugged into their browsers). To make something that acted like Flash but was driven by Perl, you'd have to write a mini-interpreter, probably as a plugin for every browser out there, and get the remote users to download and install it. Online life moves so fast it's easy to forget that just a few years ago practically no one had Flash plugins and there was quite a bit of resistance to Flash's continued existence.

So, the short answer is: no way. To make a similar kind of animation with Perl would be a monumental undertaking that would be recreating the work of hundreds of developers over several years; and it would only be an academic exercise b/c Flash (and Shockwave) have the market sewn up and getting everyone to download one more plugin would be unlikely. Even when your product is much better (eg, Quicktime vs the Windows and Real alternatives) you face enormous challenges to adoption.

update: color me wrong. See SWF::Builder.