I bought this game from GOG in the summer sale of 2014 and just got around to trying it. I had the same problem as you did. There isn't any discussion about this problem on the GOG forum, but there is a lot of people discussing it on the Steam forum. It appears that the mouse click must be very fast to be recognized. It does work, but I find myself lapsing back to a normal click speed and have to repeat clicks. I have the original disk version also, and it doesn't have this problem. I bought it again from GOG because it was dirt cheap, and I was willing to pay a little for a DRM-free copy, but it looks like if I ever play this game, I will probably revert to the old disk version, and settle for having to keep the disk in the drive.
Those flags are only to select the language, you actually start the game by clicking on the check mark below the flags. When you get into playing the game, it appears that the action menu can be opened with a normal click, but when you click on the eye, hand or talk icons, it has to be a fast click.