GOG blocks nothing here, and you need neither cookies nor the proxy capture.
The problem is the hidden javascript messing up when you are viewing the
copied offline version.

To fix it you need to edit the html pages:
sed -i 's/!isBot && !isProperCookieSet()/false/' <files>

Note: HTTrack accepts and sends cookies by default, so a cookie the server
sets is kept for the rest of the crawl.