Google Calendar and Microsoft Outlook supports this feature cross-platform. The fact that I can't use this feature prevents me from subscribing to my todo list items deadlines from TickTick, and is very inconvenient. I hope this feature sees the light of day on the web soon.

Any news on this?

It would be great if you could add this to the web app

This is unfortunately no standard yet.
It only works on the device / applications mentioned in the blog post (iOS and OS X, BusyCal).

We hope to extend that soon, but that will only work if client vendors adopt and implement it.

http://blog.fruux.com/2013/04/29/subscription-management/ is the blog post introducing this functionality. I've yet to determine whether this is an Apple API or a standard.

Is this behaviour based on a standard, or an Apple-specific API?

What is blocking its implementation on Linux/Thunderbird and Android?

This feature is indeed planned.

server side subscriptions would be so awesome.