HDR means that the image captures a greater dynamic range than a single exposure.
Relative to JPG, RAW is HDR, although yes, and it's a dynamic ranger much higher than film ever was these days (although yes, still not technically HDR).
BUT, What people output from Photomatix, unless it acually is a .hdr file are not HDR. They are tonemapped to convert HDR into a lower dynamic range that are monitors are able to display or are printers are able to print.
Exactly how much dynamic range do you consider "high"? 3 exposures 1 stop apart? 5 exposures? 7? 9? 2 stops apart? 3? I've tonemapped 11 exposure images each 2 stops apart before now to get the complete contrast range of a scene. Some do it with only 3 jpg images and call it "HDR" (which combined contain less useful data than a single 14Bit RAW).
This is what allows people to create what is affectionately known as "pseudo HDR" (creating an HDR from a single RAW file). You're not creating an HDR from a single RAW file (at least not directly, it is an intermediary), you're tonemapping data that already exists in the file into a dynamic range that your monitor can display or your printer can print.
Even 16Bit TIFF files aren't higher dynamic range than JPGs. They still have the exact same white and black point (thus the same dynamic range), they just have more shades in between (0-65535 vs. 0-255 per channel - but 65535 and 255 are both the same amount of white, which isn't noticable on your monitor until you load it into photoshop and start adding curves and effects and see smoother transitions between shifting brightness and contrast).
Proper HDR files are 32Bit and are generally used by 3D software to provide realistic lighting simulations in scenes - These are generated by Photomatix behind the scenes (although you can tell it to save out the .hdr file too), and have a dynamic range far beyond that which can be displayed in JPG or TIF images, and far beyond the display technologies of pretty much any display or print device commonly available today) and that is tonemapped to a LOW dynamic range image (JPG or TIF).