They still have HDMI because some devices can still play on the monitor and use that connection type. It's on there for compatibility.
If the monitor is HDCP enabled, then it will play everything that is encoded with a HDCP signal. It's important to have if you're buying retail copies of movies. If you pirate movies, then it doesn't matter what your devices are certified for, they will all play the pirated content.
However, if your device is not HDCP certified, very unlikely, then you will not be able to play a movie encoded with that signal. This would be a movie purchased from retail stores with copy protection on it. HDMI devices, since 2009, should all be HDCP enabled.
regarding DCHP or HDCP read this
I can play any content, copy protected or not. My setup is a Samsung S27A950D, LG blu-ray HD-dvd combo drive, and a MSI lightning radeon HD 6970.