I have NoScript set to allow everything GOG, and the download button give you a direct link anyway, so that shouldn't be an issue. It also wouldn't explain why Chrome is unable to find the download.
I'm also using NoScript, RequestPolicy, Cookie Monster, Ghostery, Disconnect, Abine Privacy Suite and several other extensions in Firefox at the moment. No problem on the download here, let me test Chrome out...
Ok, I just tested out Chrome (currently up to date), have no addons in it at all and I was able to download the current GOG downloader no problem however Chrome says "Setup_Downloader_3...exe is unsafe" with a button labelled "Discard". There is a link to more info which takes you to a Google support page that gives information on malware and phishing.
I'm going to bet that this is a false positive, but I'm going to scan the executables locally. No doubt a blue will chime in on why Chrome flags it as malware, but if I had to hazard a guess it's probably because they just updated it recently and Googles heuristics are simply not updated to recognize it as safe yet.
Ok, I scanned it with Microsoft Security Essentials and it came up clean in that at least. Not conclusive but a data point nonetheless.