Unfortunately, it's got nothing to do with the browsers themselves, but the plugin authors.
This is one of the cornerstone reasons for Apple supporting HTML5 development. Most video online requires Flash, and Adobe dropped support for Mac OS 9 development better than six years ago. Thus, even though there are few browsers that work passably in OS 9 (Classilla is a good one that's in active development, iCab was good when it was updated regularly), Flash support is gone. If HTML5 had been developed as the standard and adopted by web browsers long ago, then your OS 9 system would likely be able to handle internet video.
There is hope though, I figure. If the guys writing Classilla integrate HTML5 support, then internet video may actually work under OS 9. Not all of it mind you, but at least some of it, which is better than nothing. You could also try browsing Mobile Youtube (
http://www.m.youtube.com). That page launches all of it's videos in a separate QuickTime window, but I'm not sure if it'll work with the last version of QT for OS 9, which is also long in the tooth.