Lets try updating wine. The Mint 18.x series is based on Ubuntu 16.04 "Xenial" so that would explain why you're on wine version 1.6.2. You shouldn't need to upgrade your whole operating system for CoH (but installing the latest version of Mint would give you an almost current wine). The current version of wine is 4.0.2 as you can see from WineHQ.
I'm going to put some optional steps inside spoiler tags that I'd use to get more information, but they probably aren't necessary.
First things first, open up a terminal and update all local package lists from the remote repositories and upgrade all out of date packages with
sudo apt update
and
sudo apt upgrade
Now, confirm your current version of wine with
wine --version
We're expecting it to say 1.6.2. I don't know where you got your package of wine from, but lets assume that you used an apt repository and that Mint gets it from the Ubuntu 16.04 "Xenial" repositories.
So now we want to upgrade to the latest version of wine and that is easy because the wine project maintains its own Ubuntu-type repositories and should be fully compatible with Mint according to the WineHQ Ubuntu Installation Page.
The WineHQ installation page recommends uninstalling existing versions of wine and packages that depend on it. I would do this:
sudo apt remove wine wine-mono wine-gecko winetricks
I'll copy the installation steps from that page here:
If your system is 64 bit, enable 32 bit architecture (if you haven't already):
sudo dpkg --add-architecture i386
Download and add the repository key:
wget -nc https://dl.winehq.org/wine-builds/winehq.key
sudo apt-key add winehq.key
Add the repository:
sudo apt-add-repository 'deb https://dl.winehq.org/wine-builds/ubuntu/ xenial main'
Update packages:
sudo apt update
and install the current package:
sudo apt install --install-recommends winehq-stable
Now you can confirm that you have the newest version of wine with:
wine --version
and it should say 4.0.2 as of August 24, 2019.
Now you can try your usual method of starting CoH and see if the new version of wine solved the problem.
If not then the next step would be creating a fresh new wineprefix. wineprefixes allow you to create separate windows environments, for example for 32-bit and 64-bit, or just to keep programs separate. I think that wine will update your wineprefix environment for the new version of wine just fine, but creating a new one would ensure that it's nice and up to date.
Let me know if that fixes your current issue.
