Updated (ignored UTF warning) then tried to go to the Zenpage tab:

Warning: require_once(/home/mydirectory /home/. mydirectory/rbcphotos.mydomain.com/zen/zp-core/zenpage/zenpage-class.php) [function.require-once]: failed to open stream: No such file or directory in /home/mydirectory/rbcphotos.mydomain.com/zen/zp-core/functions-controller.php on line 30

Fatal error: require_once() [function.require]: Failed opening required ' /home/. mydirectory/rbcphotos.mydomain.com/zen/zp-core/zenpage/zenpage-class.php' (include_path='.:/usr/local/php5/lib/php:/usr/local/lib/php') in home/mydirectory/rbcphotos.mydomain.com/zen/zp-core/functions-controller.php on line 30

Okay, copied Zenpage over again but, why would anything have 'disappeared' if updating ZP doesn't include these files?

Well, zenpage consists of the folder zenpage and the file zenpage.php. If the latter is still there and is activated ZP will probably think the plugin exists. Otherwise the Zenpage tab would not appear at all.