I'm not familiar with Android TV boxes, but in general with Android 4.4 it really depends on whether the manufacturer chose to include the option of moving to SD. That was introduced in Android 2.2 (when it was normal for devices to have just a few hundred MB of built-in storage), and deprecated in 4.0, but some manufacturers retained it even though it was no longer supported. Go to Settings > Apps > Downloaded, pick an app and look for a "move to SD" button. If it exists then you have the option, though it will only work if the app allows it. If there is no such button then that's it.
Updates are the manufacturer's responsibility, so if they haven't provided one then that's the end of it. Like all mobile OSes Android must be built for the particular device (you can have generic Windows installs because a PC has a lot more resources to waste than a phone/tablet/TV box).
Rooting may give you more options, but that's at your own risk, and whether it will help will depend on how much community software support there is for your particular device. So do your research before trying that, or you may be wasting your time (and may mess up your device in the process).
As to why an SD slot, the answer is media storage, which is independent of whether it can be used for apps.
