I have a friend with macOS 10.10 Yosemite, so last version she can install is version 13.2. I'm running Mojave but I downgraded to version 13.2 as well. Get a message that the other user is running too old a version of the software. So it's clearly not as mismatch as we have the exact same version. So I have to assume the company no longer supports using this release, as the intermediary. So what version is still supported and why doesn't the web site note that while the old versions are available for download, they are useless. Not to mention show what operating systems they are for so someone can pick an appropriate download.
Using an older version of TeamViewer is only possible for our customers holding a TeamViewer license and we ask all free users to use the latest TeamViewer version available.
If possible, I recommend your friend to upgrade his/her OS to at least El Capitan (10.11) as this OS does run with TeamViewer in version 15. After that, you can use TeamViewer for connections to this device.