How could a chess computer be capable of winning against humans at chess without the terminal goal of achieving a checkmate?

Humans are capable of winning at chess without the terminal goal of doing so. Nor were humans designed by evolution specifically for chess. Why should we expect a general superintelligence to have intelligence that generalizes less easily than a human's does?

If the given goal is logically incoherent, or too vague for the AI to be able to tell apart success from failure, would it work at all?

You keep coming back to this 'logically incoherent goals' and 'vague goals' idea. Honestly, I don't have the slightest idea what you mean by those things. A goal that can't motivate one to do anything ain't a goal; it's decor, it's noise. 'Goals' are just the outcomes systems tend to produce, especially systems too complex to be easily modeled as, say, physical or chemical processes. Certainly it's possible for goals to be incredibly complicated, or to vary over time. But there's no such thing as a 'logically incoherent outcome'. So what's relevant to our purposes is whether failing to make a powerful optimization process human-friendly will also consistently stop the process from optimizing for anything whatsoever.

I think that the idea that humans not only want to make an AI exhibit such drives, but also succeed at making such drives emerge, is a very unlikely outcome.

Conditioned on a self-modifying AGI (say, an AGI that can quine its source code, edit it, then run the edited program and repeat the process) achieving domain-general situation-manipulating abilities (i.e., intelligence), analogous to humans' but to a far greater degree, which of the AI drives do you think are likely to be present, and which absent? 'It wants to self-improve' is taken as a given, because that's the hypothetical we're trying to assess. Now, should we expect such a machine to be indifferent to its own survival and to the use of environmental resources?

The point I am trying to make is that these drives constitute additional complexity, rather than being simple ideas that you can just assume

Sometimes a more complex phenomenon is the implication of a simpler hypothesis. A much narrower set of goals will have intelligence-but-not-resource-acquisition as instrumental than will have both as instrumental, because it's unlikely to hit upon a goal that requires large reasoning abilities but does not call for many material resources.

It is likely incredibly hard to make these drives emerge in a seed AI.

You haven't given arguments suggesting that here. At most, you've given arguments against expecting a seed AI to be easy to invent. Be careful to note, to yourself and others, when you switch between the claims 'a superintelligence is too hard to make' and 'if we made a superintelligence it would probably be safe'.