Since I am having problems in printing bright colors on matte coated paper with my IP8750, I wonder how come this guy get this level of brightness on uncoated paper. Maybe I should switch to a different kind of printer? If so, which one?
You can't print 'bright' colors on uncoated stock on a desktop inkjet printer because the uncoated stock just soaks in the ink.
Your sample card appears to be printed offset. Possibly using opaque inks, raised ink, a varnish, or some combination of those techniques.
It's difficult to tell for sure from a photograph, but that looks like offset lithographic printing and thermography. Basically, after printing and while the ink is still wet, the sheets are run through a machine that coats the entire sheet with powdered resin. The powdered resin sticks to the wet ink and the excess is removed by suction from the unprinted areas. The sheet then goes through a heating unit that melts resin.
It won't work with inkjet printing, since the process relies on wet litho ink for the resin to stick to it. Inkjet ink dries almost instantly.
Offset litho press with thermography unit attached, and example below.