I wrote the first (only?) GIF decoder for the Commodore 64 back in the day, including displaying animated frames. There was no 'live' delivery of images back then though; you had to download them in-full over FTP or a proprietary file transfer protocol before you started parsing. I suspect the encoding was too slow on most computers at the time to stream the file as it was encoded anyway. But yeah, the basic capability was present back then.

Once the WWW kicked off and GIFs started being served, and especially once cgi scripts started being written, someone could have had this idea and the software and hardware probably could have handled it. So we could have been doing this in the late 90's. I wish I had thought of it...

It always was actually. I even tried this on IE6 and it works