To have WordPress interact with memcached it must be installed as a PHP extension?

This depends on what is it that you are trying to do/use. In theory the protocol used to communicate with memcached server is not very complex and can be implemented in PHP, and therefor as a plugin. In practice you might want to prevent collisions of multiple processes writing at the same time to the cahce which will most likely require the access to the multi tasking API of the OS, something that is not built-in in the default PHP modules and will require you to use additional modules in any case. (there is also probably some performance argument that can be made here between running C and PHP code, but I am not sure how important it is).

Having it as module also let you as the server admin “break out” of whatever restrictions you put on the PHP code in the php.ini and other setting files (in theory you can block the ability of the PHP application to connect anywhere, although I never heard of anyone doing that)