In the example above, the description says a state of non-equilibrium of chemical balance exists (although I've no idea what that means) so does terraforming not make this umm... become equal?
No, definitely not.
If you want to end the non-equilibrium of chemical balance you need to hit it with high-energy weapons, a really big rock, something like that - wipe out all life - then wait a few millenia for the dust to settle. Basically you "shouldn't" have free oxygen in an atmosphere in any non-trace quantity, because it reacts with almost anything. So if you have free oxygen, something is pushing the atmosphere out of a purely chemical equilibrium - loosely speaking, a plant, whether natural or industrial - to continually create that oxygen. Equilibrium is stasis. Life is change.
ELWs in Elite Dangerous are ones with an atmospheric composition, temperature and pressure that's survivable without further assistance by human life - this may be a natural occurrence, or terraforming may have been used to adjust a planet which was further from that state towards it: either way it requires something to be continually generating the oxygen and putting the atmosphere out of chemical equilibrium.
I would say that "Water Worlds" are semi-Earthlike: they've got broadly the same water-based life, but the atmospheric composition would kill an unshielded human relatively quickly (might be weeks rather than minutes, for some of them) ... while Terraformable High Metal Content worlds are in the right temperature range (or would be, with a human-breathable atmosphere) but don't have any significant life to adjust atmospheric composition.
(The trace lifeforms like Bark Mounds - and the equivalents found on the tenuous atmospheres in Odyssey - probably aren't putting the atmosphere out of chemical equilibrium due to their sparse distribution ... and the lack of an atmosphere ... but they may be doing something similar to the ground they rest on)