A post on Pantheon's Q Spear Shot in the official forum labels it as an execute. I tried to read the description and so far, I'm under the impression it is just the 50% extra damage for low hp targets but there is no additional damage per missing %hp similar to e.g. Demacian Justice (Garen's ultimate)
Are there other changes I'm unaware of that added execute mechanics to this ability, or am I just confused about the meaning of the term itself?
"Execute" isn't an official term with a set meaning. Generally, it's just used to refer to skills that tend to be situationally good for dealing the final damage to an enemy champion to kill him.
Garen's Ult is an "execute" because it deals extra damage based on missing hp, and Pantheon's Q is an execute because it deals extra damage to low HP targets. The mechanics aren't identical, but they both generally lead in the same direction: you can use them to finish off a low-health champion.
Cho'Gath's ult is also a good execute, because it's best situationally when the enemy will die from the hit, even though it doesn't get any bonuses at all based on enemy health.
