It will display HD movies with no issues. And yes, you can call it an "HD Monitor". HD is really just a cool term everyone uses now, like PDA was last decade, or "Broadband". Your monitor does not need to be labled "HD" to be able to display those resolutions.
HD means only 'High Definition', which is considered to be any resolution above 720p. The concept of high-definition itself has absolutely nothing to do with HDMI, which means High-Definition Media Interface and thus is only a type of connection.
To clarify things, remember that you can dislay any low-definition media thru an HDMI connection, and as well you can display any "high-definition" media thru any interface other than HDMI.
So, while your monitor does not have the "most appropriate" interface for it, it will definitely display correctly the high-def media you want to throw at it.