Access standalone GUI application through Web
The only way to make something like that possible would be to load the application into memory, interact with it and render the presentation. Consider something like having a application that can parse a HTML document, instantiate and provides access to the DOM elements in memory so that you can modify their properties and then render it's current display. 
That's too much to ask. Consider the fact that you'll have several users concurrently requesting the application to render several different sates, where you'll potentially have to manage several instances of the application so that you don't block requests. I would look at potential alternatives, reimplementing the application for the canvas element, or perhaps Flash or Silverlight.
Is it possible to access a standalone GUI-based application over the Web? The concerned application is an event animator, which displays the animation based on custom textual inputs.
I don't wish to access that software through any remote desktop connection (or web meeting) like option. I actually intend to integrate the software with my existing web-application. So that, based on user inputs in the web page, the software should be able to display animations of relevant things. Please note that it won't be possible to achieve the functionality using JavaScript or something else -- in that case I've to recreate the application again. Also, the software runs in an interactive mode. It doesn't provide to generate any GIF or video file using any command line argument.
I'm using Python-Django for development on Linux.