According to https://en.wikipedia.org/w/index.php?title=TimedText:Meghan_Trainor_-_N%C3%98.ogg.en.srt&action=info, the content model is wikitext.

The check that fails is here:

var isViewPage = mw.config.get( 'wgIsArticle' ) && !( 'diff' in uri.query );
var isEditPage = mw.config.get( 'wgAction' ) === 'edit' || mw.config.get( 'wgAction' ) === 'submit';
var pageCanLoadEditor = isViewPage || isEditPage;

Specifically wgIsArticle is false, so this is not considered a "view page".

Given that this is a wikitext content page, that sounds like a bug in TimedText.

Change 787786 had a related patch set uploaded (by Esanders; author: Esanders):

[mediawiki/extensions/TimedMediaHandler@master] TimedTextPage: Call setArticleFlag

https://gerrit.wikimedia.org/r/787786

The above patch also adds "Permanent link" and "Printable version" to the sidebar, along with anything also that depends on the article flag.

I would have never thought to look for that. Thank you Ed !

Change 787786 merged by jenkins-bot:

[mediawiki/extensions/TimedMediaHandler@master] TimedTextPage: Call setArticleFlag

https://gerrit.wikimedia.org/r/787786