The dwarf is a big nuisance because he will steal items from you. The item he takes is random, but often you can not get the item back. Some of the items, such as the lost treasures, are show stoppers if stolen and you will not be able to finish the game without them.
While in Daventry, you can usually avoid the Dwarf by moving quickly through areas he appears. If you are on the cave boardwalks leading the the Giant's Cloudland, it's much harder to get away from the Dwarf. There, your best protection is the invisibility ring. The protection spell works as well, but it's hard to move fast enough to complete the boardwalks before the spell runs out—especially if you have to come back down.
It is said that the King's wife became ill, and a Dwarf claimed he had a special root that would make her well again. For this root, the Dwarf wanted Magic Shield. The King complied, but the root did not cure her and the Queen died. Perhaps this is the same Dwarf You won't be able to do anything to the Dwarf in King's Quest I, but you do get to in King's Quest II.