Do it like they did in the good old days when JS was new and couldn't be relied upon to exist.

Don't rely upon it to exist.

Serve up well marked content, CSS that might format it nicely, and JavaScript that allows some types of per-validation to happen client side but only as a means of making a page nicer. The server side should STILL perform all data validation, normalization, and verification (assume someone will craft their own form submission).

No, Twitch specifically. It's an interactive chat and live video streaming application that happens to be built out of web tech. If you don't have AJAX, you could maybe-kinda-sorta kludge it together out of forms and video elements, but it'd degrade hard, and need to be built completely different from the normally-interactive version.

I was thinking of Twitter for some reason.

Twitch could be done with a native app... the phone versions SHOULD be done with such if they aren't.

How is installing a native application a viable alternative to javascript? Presumably, if you're blocking the latter is because you don't want to run untrusted code on your device.

Twitch does have an IRC gateway, so it's possible to use your own application for chat.

As another poster commented, the video aspect can be fulfilled with a number of different methods, and I don't see any technical reason a standard couldn't be followed to allow for arbitrary clients to handle that interaction as well.

We had chat long before the era of SPAs -- no JS was required with things like long-polling, although that's one of the applications where I think a bit of JS will definitely be useful and welcome.

As for video streaming, that's not hard at all, especially now that there's a <video> tag.