Had the same problem with Battle Brothers. "Buying" the free DLC (Of Flesh and Faith) solved it. Doesn't make any sense, but hey.

I'm having the same problem with a new purchase of Maniac Mansion. In fact, trying to download the offline installer also fails with this json:

{
"error": "invalid_licence",
"error_description": "User #XXXXXXXXX does not have the license for product #1832758895."
}

(user number removed)

I just had same issue with Fallout 4 GOTY - starting GOG as administrator (right click - start as administrator) fixed the issue.

Had the same issue.

I noticed it was always getting to 2% before failing and the option was only to retry the install. I went to "manage installation" and uninstalled it. After that the installation worked.

It could have been opening up the firewall that actually fixed it, but it needed the partial installation removed before it would work. I did not have the bandwidth limited so it wasn't that.

While opening the firewall I noticed some other programs had simply added themselves during their installation. Not sure why Gog can't do the same.