SirPrimalform: Hmm, if running as an administrator helps then I'm fairly certain the problem is being caused by UAC, but beyond that I have no suggestions.
Tusal: I am still waiting on GoG's response to my ticket; thank you for your replies in the mean time--I appreciate it.
That being said, what conclusions do you draw about the new directory solution and the seemingly UAC issue? The OP says when he reinstalled he didn't have to run as administrator.
Also, during the install I cannot direct the installer to my DOSBox folder; when I do, it simply doesn't recognize that DOSBox & it wants to install it's own DOSBox within the PQ:SWAT2 directory. Not sure how relevant that is to the issue, but one reason I necromancied this thread was to hopefully provide a working solution at some point, so including all problems I'm encountering seems logical.
Well that's the thing, UAC is the cause of the original problem in this thread (UAC prevents programs from modifying anything in Program Files, something that some older games require to run). Installing outside normally fixes this because they are no longer restricted, but it seems like that restriction isn't being lifted in this case for some reason.
The DOSBox thing you mention is due to you having a different (and probably more recent) version of DOSBox than the one the installer was made to recognise. Instead of updating/fixing that option, it seems that GOG has opted to remove it from more recent installers. =(