I noticed that the description for some artifact abilities, specifically, Asmodeus's, Lyphia's, and Evelyn's, have an ability called 'Devil' along with the other abilities. The skills are #153, #158, and #159 respectively if you wish to look them up. Does anyone know what 'Devil' concretely means in the description?

That should be checked, but from informations I gathered, I came to conclusion that "Devil" is in fact "Elemental" skill (and it's rather hard to check whether it's true or not).

It's probably the 'elemental' skill. The Japanese term of the skill was 魔人特性 which roughly translates to 'devil's characteristic'. That's probably where the 'devil' is from.

Actually, if you go to Info -> Skill -> 153 Devil's play, you'll see the word 'element' in the description. The other's don't have it though.

First, let me point out that acording to japanese wiki 'Elemental' skill in japanese is 魔神特性 (probably).
Now, if Devil's Play actually have 'Element' in description then our problems is solved, because once again acording to japanese wiki Lyphia's, Evelyn's and Asmodeus' accessories all have 魔神特性 skill. However last time I checked Devil's Play also had 'Devil', not 'Elemental' in description and I may have translated something wrong.
The best way of checking it would be equiping accessory with 'Devil' in it and checking whether you get damaged by some lvl 90 maps (for example Mirage Forest/Burning Sands damage your character every turn if don't have Earth Blessing equiped, and Elemental skill should provide Earth Blessing).
Also, Elemental skill have some kind of demon/devil in its picture.

This is what I meant:

So it appears that Devil = Elemental.