In SharePoint 2010 the termstore management link is available for site owners by default. This link is missing in SharePoint 2013 for site owners. Being a site owner, they should be able to navigate to the link in site settings.
The first thing to check is if you have the permissions (Owners) on the site. Validated the same and the link is still missing.
After some testing I found out, that the permission causing that issue was “Apply Themes and Borders” at web app level. In central administration navigate to manage web applications, select the application where you have the site collection created. In the Ribbon select User Permissions and check for "Apply Themes and Borders". Once this permission is checked navigate to site collection>> site settings. you will now see the link.
I cannot see any relationship to the Term Store Management functionality, but as soon as I granted that permission to the users, they would see that link. Strange! I would be glad if someone has an explanation for that. Microsoft describes that permission as “Apply a theme or borders to the whole website.”
In case this permission needs to be unchecked then only workaround is to navigate the URL “/_layouts/15/termstoremanager.aspx” to the users. As this is the case for us too.