You're not missing anything. You're right. You can use either DVI-D to connect your 144hz monitor to your PC's Video card, or a DisplayPort (DP) cable. You shouldn't use both. And honestly I'd use DP because of the higher bandwidths and future compatibilities like newer graphics cards. DVI is on its way out of the market.
You will have to supply power to the monitor too, so hence, it needs its own power cable. Maybe someday power will be supplied to the monitor through the video cable, but alas, that day has not come yet.
Also, that monitor has HDMI ports... You *could* use those, but HDMI was meant for Televisions and home theater devices, yet its infected the PC market in its greed. Not to mention the cables are still being sold at...