Ok! So I just went back and re-read what I wrote in those threads the last time this came up, and refreshed my understanding of these rules.
So! As the rules and card are currently written, Blue Gremlin Teleports as a move action.
This means that it fulfills the Charge +X requirements because:
1. It takes its move action.
2. It moves, because Teleportation is included in the category of "movement" which includes taking normal move actions, teleportation, and push effects.
Consider, for example, the FAQ section on Traps:
Traps: A creature only “enters” a zone if it moves there (either uses a move action or is Pushed or Teleported). Being Summoned or otherwise put into play in that zone does not count as “entering” the zone and will not trigger a trap.
Or the definition of Teleport in the rules:
Teleporting is an effect that moves a creature directly from one zone to another.
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BUT!
The last time this came up, Alex Mont said,
The next rules update will change some of the terminology about movement related actions, specifically to clarify this type of situation.
The way we are planning to do it is that Blue Gremlin's teleport ability is not actually a move action; it is something you do "instead of a move action". This means that it counts as a move action for the purposes of what actions you can do in a round, but does not count as a move action for purposes of Suppression Orb, Restrained, etc.
Similarly, the use of the "Climbing" trait counts as a full action for purposes of what actions you can do in a round, but also counts as a move action for purposes of Suppression Orb, Restrained etc. (We don't want it so you can climb while Restrained!)
If and when that change happens, Blue Gremlin won't be able to get the charge bonus by teleporting, because instead of taking a move action, the Gremlin will teleport "instead of taking a move action." Since the Gremlin doesn't take a move action, it can't get the charge bonus.
