This is interesting. I'd say it should definitely train two-handers.
Aotme for example is a massive two-handed artifact axe and yet it trains two-handed weapons instead of axes.
I'd say for the sake of consistency, the same logic should be applied to the hammer of gods, or the hammer be made one handed.

Relevant issue.

It might make more sense if the Two-handed group was removed entirely, and any twohanded clubs use the clubs skill, any twohanded axes use the axes skill, any twohanded polearms use polearms (as they do already), etc... unless of course Twohanded skill granted far higher bonuses.

Adom manual says:

"Twohanded weapons are specifically built to be used with great strength. Thus you receive one-half the standard damage bonus from strength as an extra bonus when wielding a weapon of this category (and only this category - other weapons like staves and polearms are built differently)."

So for example if you use a scythe you get more angular momentum (and reach) from the long shaft, but can't manage your strength optimally because the shaft is not that sturdy and you might have balance issues. Hence it's a polearm in spite of requiring two hands to use. Whereas a 2-H sword is specifically made to maximize the effect of strength, and the weapon skills category reflects an ability to use that to your advantage.

The Hammer of the Gods behaviour is consistent with huge iron hammer, which also is a heavy weapon requiring two hands, but not optimised perhaps to be used as a weapon. I would imagine a huge heavy hammer isn't exactly a well-balanced weapon to wield like a 2-H club, axe or a sword might be. The minotaur axe could be balanced for strength much better. In that sense, even though the hammer is so heavy that you need two hands, the fighting technique still has to take into account the problems of having a lump of iron stuck at the end of a stick. Following this logic, it's not a bug but a feature.

(Although you could also argue that the hammer of Thor is supposed to be good both for throwing and striking, and this weapon with the returning and immunity properties is a nod in that direction)

The only issue I have with that is that an Axe, or a Club, is often a long stick, with an axehead or club head on the end. The exception being a wooden club, which is essentially just a broken tree branch or in the case of trolls, a small tree.

Also, many hammers are often well-balanced, so that one can use their full strength behind the blow. That's why most hammers and maces have a counter-weight attached to the hammer head to balance out the swing. Afterall, the twohanded mace or hammer was often the best way to inflict maximum damage twohanded, in other games, so why not here as well? Like take the good old carpenter's hammer in today's world. There is a reason why it has that extra nail remover head attached, as it provides a good counter-weight to the hammer to make best use of a person's strength.

The text in the manual, and Feorg's interpretation, make sense to me. But if the game is going to stick with it, then the skill in "Two handed weapons" should be renamed to something more precise, like "Heavy weapons" or something like that.

Right now, there is a category of items in the inventory called "Two handed weapons" for the weapons that are, well, wielded with two hands. So it is counterintuitive that a skill is also called "Two handed weapons" and it doesn't span exactly those weapons. I think the name change would fix the incoherence without much fuss.

Seconded. Two-handed weapons category was bothering me always as well. It's just not clear without googling, testing or reading manual which skill will train and use "Two-handed sword" - two-handed weapons or swords.

I agree with argumentation above but something has to change to make game more intuitive. Either wording or mechanics.