An enemy shifting meets the criteria for enemy movement and would trigger this power. From the Rules Compendium glossary p314, or DDI.
Move: Any instance of movement ... Shifting, teleporting, and being pushed are all examples of moves.
There is a bit of confusion in your question though. You are asking about
Opportunity Actions. Pursuit of the Hunter triggers an
Immediate Reaction The two are different and should not be confused. As an example, if a creature did a non-shifting move away from the Ranger, the Ranger could use an Opportunity Attack against the creature and then use Pursuit of the Hunter as an Immediate to move himself.
@BrianBallsunStanton thinks that using this power to shift out of flanking is likely against the Rules As Intended. I do not believe this interpretation to be correct.
The section quoted
Your prey tries to maneuver away, but there is no escape.
is flavor text. Flavor Text is defined on p62 of Heroes of the Forgotten Kingdoms, includes this bit:
Feel free to invent a description of the power yourself
Also see Dragon Magazine #394, Reflavoring Powers
choose how their characters’ powers act,
customizing each for the theme of the character or feel of the campaign.
Based on the above, I believe it is clearly intended for players to use the descriptions of the powers as a help to understand how they might look. For a DM to disallow uses of a power that do not meet with the flavor text but is otherwise legal would not be correct and such rulings should be known in advance so that the players can accomodate them.