Note that the FAQ says spell-like ability. The Shift ability is supernatural, not spell-like, as is indicated by the (Su) right after it. So you cannot use it to qualify for dimensional agility.
Dimensional Agility + Teleportation Sub-School Shift power, Where can I find the FAQ?
There doesn't need to be an FAQ.
You're using a Supernatural Ability with Shift.
Dimensional Agility only works on either Abundant Step or when you cast Dimension Door.
Since you're not using Abundant Step, and you aren't actually casting Dimension Door, even as a Spell-Like Ability, Dimensional Agility just sits there doing nothing.