Is fall damage only calculated on vertical distance?

Question

From this answer to Is damage taken when falling off a mount?:

The minimum distance to take fall damage is stated as 10ft.

However, if you are on a fast mount, you could potentially fall off while moving rapidly. In this case, you will have a significant amount of forward motion before hitting the ground. It's not clear to me whether this distance should be included in deciding whether fall damage applies (RAW).

Does fall damage only include the vertical component of a fall, or is the total distance applied?

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As an example:

On a 6ft horse, dashing, the player can be moving forward at 120ft/turn (20ft/second).

If they are to fall, they will take 0.61s to reach the ground (6ft drop), and so will travel 12.2ft forward as well as the 6ft down (hypotenuse ~13.5ft).

As the forward motion is significant, and exceeds the 10ft minimum for fall damage - should the player take damage from this fall?

Answer 1

Vertical Distance Only

The relevant rule:

At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. (SRD p.86)

By RAW you only take damage for the distance you "fell". So the question then becomes: What is defined as a fall?

Seeing as the rules don't define it for us, we can look to the common definition of the word "fall". According to Merriam-Webster and accounting for context, that would be:

1. to descend freely by the force of gravity

Since a fall is defined specifically as the descent brought on by gravity, then only the negative vertical component should be considered. You don't count the horizontal component in the same way that you don't count the vertical "up" distance traveled prior to reaching the apex.

Bonus Points

The Reverse Gravity spell also helps strengthen the definition of fall as down relative to gravity:

All creatures and objects that aren't somehow anchored to the ground in the area fall upward and reach the top of the area when you cast this spell.

...

If some solid object (such as a ceiling) is encountered in this fall, falling objects and creatures strike it just as they would during a normal downward fall.

Answer 2

I'd argue that the damage people receive traveling horizontally is pretty minor (in most cases). I once dropped my motorcycle going 65 mph and walked away with only scrapes. At most, damage done falling off the mount could be considered nonlethal damage (if you homebrewed nonlethal damage into 5e, but you're asking RAW so no?)

Now if they were to "fall" head first into a brick wall one could justify fall damage in the horizontal plane seeing that falling damage doesn't come from the fall itself but the sudden stop at the bottom.