Though those sites offer CC Chinese subtitles, the LingQ extension doesn´t work for them. Do you know any hacking for that?
I don’t think there are political reasons for this. There are also countless (Western) streaming services that remain unsupported, for example Amazon Prime Video, Disney+, Hulu, Peacock, Disney+, HBO Max etc. I assume LingQ just doesn’t have the (development) resources to support more sites.
I don’t really watch many shows, but there are 3rd party sites that allow you to download subtitles, at least if they are not paywalled, https://downsub.com/ seems to support quite a few of these streaming sites.
You could also look for a browser extension, maybe something like Greasemonkey / Tampermonkey. Or give yt-dl / yt-dlp a try, maybe you’re lucky and they support one of the sites.