I thought this thread looked familiar!
No need to hate yourself (even temporarily), as the 4870 card is the HD 4870. All of the manufacturer's above are different, but are making the same card. Sure it might look a little different, and have a different cooler, but they are all the same. They follow the one reference design to be allowed to call it the 4870.
I find it weird that DX10 isn't on the disc, though. DX10 should automatically be installed with Vista if it detects a DX10-compatible video card.
Either way, you should be able to download it from the Microsoft website.
ASUS are a great card manufacturer, you should have no problems with it. ANY 4870 will support DX10.
Although HIS is one of my personal favourites, they're great! That's just opinion though, and no reason why not to choose (or be happy with) ASUS instead.
And make sure you write to the manager, with a well-worded letter to ensure you get your leather mouse pad. Don't let them get away with it! (If it was part of the deal, that is).