Again, you're looking at a very narrow scope for the question you're posing. It's not gaining energy at all, since the Earth would be exerting the same amount of energy on it regardless.

Had your wormhole pulled it from a pure vacuum that cannot actually exist in real life, your 'misguided notions' would be correct. However, the energy in the system has not changed at all; the location of your theoretical billiard ball has. Now if we extrapolate the energy distribution over time across a large timeframe, unless we'll assume that that billiard ball is undergoing infinite "nudges" into said wormhole [all of which you're conveniently ignoring as energy going into the system], then that ball falling in a single instance is no different from one at a standstill in reference to the Earth.

For such a theoretical, large scale question, you sure are focused on the minutiae.

And wouldn't it be better just to use Newton's Laws, which the laws of thermodynamics are derived from anyways..?