Being a dwarf is a state of mind. It is composed namely of greed, being quarrelsome, ingenuity, and thoughtlessness - yes, you must be smart and stupid at the same time, and this conflict is the core of the dwarf.
Dig deeper. Deeper still. Can't go deeper? We know tricks to solve that. Mine ALL the ore! Claim ALL the socks! Seize ALL the elven animals! The world is yours. It is not yours for the taking. It is already yours! You just haven't moved it all within arm's reach, yet.
Build it bigger. Show off what you've got. Don't just sit on that gold, make gold blocks and build walls. Don't just slash the enemies with a steel axe, slash them with a steel axe studded with silver! Statue isn't a masterpiece, melt it and try again! Higher skill, higher value, proclaim your wealth. Proclaim yourself better than everyone else. When they come to complain you shove a spear in their gut. Even if they don't come to complain, and the come with those donkeys, you shove a spear in their guy anyways! You're a Dwarf, you laugh in the face of danger, even if you have to take the train outside of town and knock on danger's door while danger isn't bothering anyone.
A single boulder into a whole workshop? How do you make booze from a plant within 3 hours using only an alder log and a barrel? How did you turn a single rock into a whole wall section? How did you turn a single bar of metal into an entire statue? For that matter, how did you build such architecture, or do such engravings of engravings of engravings of cheese? The Humans piddle with walls, you piddle with obsidian machineguns and magma land mines. The world is a machine and you its mechanic, with all the tinkering and construction just a simple movement before you bend the whole world to your whim. If you want it to be done, then you may do so. You don't look at the sky and sigh. You look up, and then you cast raw obsidian in the clouds because nothing is beyond your ability. A handful of stones is all you need to churn a river into an impossible liquid sinkhole. There are no limits to dwarven ingenuity, even nature itself. Anything named impossible, simply isn't fully explored yet.
But yet, above all else, the Dwarf is stupid. Rush to get socks during a battle. Fall asleep at the lever. Go On Break when your patient arrives bleeding and screaming. Carry your baby into battle. Even beyond that, the dwarven hive mind is stupid. There is no need for practically anything, in fact most times causing injury to dwarven life as a whole. Obsidian casting costs lives to achieve a mere wall that the masons could have produced just as easy. That silver-encrusted armor needed to buy the silver with booze that could have sustained a dwarf for twenty years! There is no point to these things, no logic, just the incessant piddling of a child genius who giggles at the word "penis" and is smart enough to build a cast obsidian penis in the middle of the air.
That, is Dwarf. In this regard, any creature may be a Dwarf, regardless of what the creature actually is. See: Cacame, the Elven Dwarf.