Hello Marcie,
Thanks for your question -- unfortunately I'm not sure we know the answer! If you can see the video in your Web browser on your computer, and if you can normally "cast" your Web browser to your TV (e.g. with a Chromecast), then I would expect you can cast the Puffer website just like any other website.
Or if the Roku has its own Web browser that supports the MediaSource extensions to JavaScript, perhaps it can visit
https://puffer.stanford.edu itself without needing to "cast" from a computer at all.
I think if somebody comes along and writes a Roku app for Puffer, this would become a lot easier. But we haven't heard of anybody who has done this.
Sincerely,
Keith