At the bottom of that link[1] you can find instructions on how to send notifications directly from your server, but it involves recompiling the apps (which is hardly Zulip's fault).
Yes, this was covered under our evaluation, I appreciate it's not your fault.
For what it's worth Zulip was at the top of our list when we evaluated hipchat replacements.
Happy to look at it again if you ever will have direct notifications.
