The Way of Shadow monk's Shadow Step feature says you can teleport up to 60 feet to an empty space from one dimly lit or dark space to another. Does that include the ceiling of a dungeon?

Thematically it fits for a ninja to appear along walls/ceilings. But does "empty space" mean ground necessarily according to the rules?

Abuse case (rather than use case):

I'm playing a Way of Shadow Loxodon. I plan to Shadow Step to the ceiling above a creature to crash down on top of them with my roughly 400 lbs of Elephant-man.

Is this legal? (Yes, DMs can rule whatever, we've already figured it out for our group. I want to know if it is officially illegal to Shadow Step to a ceiling within range.)

If they can see it, it is legal to teleport to the ceiling

When you are in dim light or darkness, as a bonus action you can teleport up to 60 feet to an unoccupied space you can see that is also in dim light or darkness.

As long as nothing else is occupying that ceiling tile and you can see the space, you can teleport there. There is nothing that specifies any kind of restriction to the direction or place that is valid for teleportation. You don't even have to teleport to a solid surface. You can teleport to a space in mid-air if you wanted to. Spells/abilities that limit themselves to the ground for example explicitly say "ground" in the description.

Damaging your opponent by falling on them is completely up to the DM

Nothing in the rules says that creatures take damage from another creature falling on them or how much that damage should be. Your DM will have to adjudicate this.

Note, however, that since you are falling, you are going to take fall damage for sure. From 60 feet up you will take up to 6d6 of damage (depending on monk level, you may be able to reduce this). Depending on how your DM rules, you may actually take more damage then you do to your opponent.

Yes, it is legal

The Way of Shadow monk's Shadow Step feature (PHB, p. 80) says:

At 6th level, you gain the ability to step from one shadow into another. When you are in dim light or darkness, as a bonus action you can teleport up to 60 feet to an unoccupied space you can see that is also in dim light or darkness. You then have advantage on the first melee attack you make before the end of the turn.

An unoccupied point in space is an unoccupied point in space. There's no clarifying rule that it requires ground beneath your feat. Clinging to the ceiling is a different matter that your DM will handle, but merely teleporting there and falling is a simple matter.

Shadow Step is made to cover great distances and allow cool maneuvers. And a Bonus Action isn't nothing either. Most of your monk features require this bonus action, so you're making a trade-off with this idea.

How much damage both of you take and why depends on the context you use it in and what additional features you decide to use. That calculation is generally outside the scope of this question. Similarly, if and how you can cling to a wall or ceiling is also outside the scope of this question. Shadow step doesn't stop you from clinging to anything, though.