For your Fortifi Live Chat client to appear on your site, you need at least one Support Agent online and available for Live Chat in order to answer any chats that are started.
To do this, any employee who has the Support Agent role can click on Support and then Live Chat to get to the Live Chat page.
In the top right hand corner there is a toggle they can switch to "Available":
With this done the Live Chat client will be available on any web page it has been enabled on, and any Chats which are started will appear in the Queue for that Support Agent:
You can have as many Support Agents online at once as you want, with each of those employees setting themselves to Available.