I haven't looked at pushpin yet, but I'm writing this answer to point to another framework that supports non-blocking applications in PHP:
React http://reactphp.org/
It supports binding a server to HTTP, or WebSocket and can be used with webserver software such as Nginx by forwarding (using proxy_pass) requests to it over HTTP. You can even use HTTPS in the webserver and forward that non-encrypted. (SSL support in React is lacking.)
There doesn't appear to be FastCGI or UWSGI support yet, at least not in the upstream project.
The style is similar to writing node.js, you attach PHP 5.3+ closures to events, and it uses the non-blocking sockets transparently underneath. There are good examples on that website, so I won't repeat them here since you didn't ask for a use case specifically.
UPDATED: I just looked at the pushpin website and it's not a framework or tool for writing non-blocking PHP applications as requested in the question title. It does seem like it would be useful as part of a solution though.