Those spindly extensions are Wi-Fi antennas, meaning the card can transmit its video signal over thin air. Why, you may ask, would I want to do that? The thinking is that it lets people separate their monitors from their computers, so all you need to work is a screen and a mouse/keyboard, and not the whole kit and kaboodle.
While that may sound a bit stupid, there are a few scenarios where it’d come in handy. Like a media centre rig where you don’t have enough power outlets for a TV setup (along with consoles and sound) and a PC. Or if you want a monitor somewhere you wouldn’t want a computer lying around, like the kitchen or a workshop.