The fan is analogous to the antenna - it changes the RF landscape, such that a small amount of energy that would otherwise have stayed in the transmission line begins to flow into the antenna, similar to how the fan changes the air current landscape.

Is this similar to "transformer action"?

Wouldn't this be the same or greater if the fence is grounded?

Would this still be the case if the power lines were properly isolated?

It feels a lot like spillage to me, antenna or not, but I admit my emf is weak

From a physics perspective, the initial analogy doesn't hold at all though.

The antenna array is actually distorting the electromagnetic field and whatever is plugged to it is actively draining power from the power line. If there's no antenna the power line lose no energy through the field[1], it's not as if you were collecting lost power.

[1] in fact, you can even say that the energy is not carried in the cables themselves but in the air surrounding the cables!

Would that be the case if the power lines were properly isolated?

Define “properly isolated”. From the electric current perspective, the cables are properly insulated, and the insulating material is air. But here what's at stake is electromagnetic (EM) waves generated by the oscillating current flowing throw the cables, and while EM shields can reduce these I'm not sure it would even be possible to shield an entire cable in order to contain the field, and even if it was theoretically possible, it's almost certain that it wouldn't be realistic at the scale of a power grid.