> So, that would mean that the d-scores in the .dat file are already in the right format and need no further analysis, right?
Yes.
> However, if that's the case, I'm kind of curious as to why that SPSS syntax is still offered on the IAT Task Library page, if one actually does not require it.
To double-check the results, offer a starting place for further analysis, etc. etc.
> I mean, if one were to use that syntax on the present .dat file, wouldn't all the extra calculations change the data from the already correct scores into something different?
No, why would that be? The scores are calculated from the raw latency data (latency column), it doesn't matter if there's expressions.d etc already in the data file. Read the SPSS syntax for yourself to see how it proceeds.
> Also, is there any notice anywhere on Millisecond of the fact that Inquisit already outputs d-scores according to Greenwald's improved algorithm, for citation purposes?
It's discussed at great length in the very topic you referenced:
https://www.millisecond.com/forums/Topic3444.aspx. Not sure what you mean by "for citation purposes", properly citing the work you use (here: Greenwald et al. 2003), would be up to you.