You elf-loving so and sos....the dwarves are the victims, here! Why doesn't magic like dwarves? Huh? Ask yourselves that!
Ahem.
Tolkien's world is only one basis for the D&D dwarf, as has been mentioned. More importantly, the D&D definition of a 'magic item' is pretty poor for such items in Tolkien's world.
Sam makes comments about just that as the group prepares to leave Lothlorien in 'Fellowship'. The elves don't view what they do as 'magical', and truthfully, they aren't. They're just so amazing (the elves and their creations) that to non-elves, they seem magical. A bow so well made that it always strikes true, a cloak that makes the wearer seem to become part of his surroundings or a sword so well made that it feels the evil of goblins and reacts to them...the elves don't see these items as magic...though clearly the hobbits do, even down to the rope and bread the elves make.
The dwarves, by extension, are much the same. Their creator is the valar of smiths, and they carry his tradition. They too crafted great items of value and skill. The mitrhil shirt that Frodo wears is not magical...but it seems so to those unable to fashion such. Again, the dwarves of Tolkien are craftsmen beyond belief, creating items that are magical without actually being magic in their eyes. The door to Moria, though, may be an exception, as it may possibly have been crafted by both dwarves and elves.
Note, though, that the most powerful items of Tolkiens world are either divine (the silmarils) or forged by Elves and Sauron, not dwarves (the rings)