If you are a Unity user, then a web player plugin is installed when you install Unity. Otherwise, the download you fetch from our website delivers just the plugin component. The first time that use this plugin, it'll connect to Unity servers to download the player and mono runtime components. This means you need to be connected to the internet.
There are some "full" installers kicking about, bit it's hard to know where you get them from, and which plugin version they contain. Also, web player plugin use does require analytics to be enabled, which does mean you are online.
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