What is an ability is not defined by a game term.
Skills represent some of the most basic and yet most fundamental abilities your character possesses.
Skills are considered abilities for all purposes where the rules references simply to "abilities".
We can see proof of this on a bunch of texts scattered through the books An example being the Downtime Rules from Ultimate Campaign:
This section explains the basic game terms for the downtime system. It uses existing character abilities (such as skill checks and saving throws), familiar resources (such as gold pieces), and new resources specific to the downtime system. Together, these allow you to accomplish tasks.
Or even on the Core Rulebook, when defining Feats:
Feat: A feat is an ability a creature has mastered. Feats often allow creatures to circumvent rules or restrictions. Creatures receive a number of feats based off their Hit Dice, but some classes and other abilities grant bonus feats.
Special Abilities, on the other hand are defined as either Extraordinary, Supernatural or Spell-like. So if an effect calls for special abilities, it must be referencing to abilities that are either Ex, Su or Sp.
But otherwise, everything your character can do is considered an ability.
There is more information about abilities on this thread on paizo's forum.
The Psychic Inception says:
Psychic Inception: The hypnotic stare and its penalty can affect creatures that are mindless or immune to mind-affecting effects (such as an undead or vermin). The mesmerist can also partially affect such a creature with his mind-affecting spells and abilities if it's under the effect of his hypnotic stare
As defined on this FAQ entry (thanks @Detterm for pointing this out), Intimidate applies a fear effect and is also considered a mind-affecting ability, and fully qualifies on the restrictions of Psychic Inception.
Unless an errata is issued at a latter date to fix the text of the ability, Psychic Inception does affect Intimidate.