In order to get mailto: links to open in Hiri you need to register it as the default application in your desktop manager.
If you installed Hiri snap package, it will already be in the list of default applications. So in Ubuntu 16.04, you only need to open Default Applications and under Mail select Hiri, like so:
If you installed Hiri from the tarball, the procedure is slightly different. In Hiri go to Settings -> General, scroll down to Desktop Integration and click Register as default mail app.