asciinema stream feature has just landed: `stream` command by ku1ik · Pull Request #611 · asciinema/asciinema · GitHub
Currently the local-only (local web server) mode is implemented, which starts a local web server, serving a page with the asciinema player automatically connected to the live stream.
If you’d like to play with it then follow Testing the new Rust version of the asciinema CLI - #10 by ku1ik
Next implementation step will be the forwarding mode, i.e. proxying the live stream via a remote asciinema server.