In the screenshot above when an Analyst selects the "Create New" link a new Incident would be created, as noted to the left of the Create New link.
Depending on the role which the end user is logged in under will determine whether an Incident, Request or Issue gets created.
Since the end user who initiated the chat was logged in under an Employee role, the ticket type will default to Incident.
If the end user was logged in under a Customer role, then this would default to Issue.
The analyst who is chatting with the end user can then select a template, either SA-Resolved which would show up as a closed ticket for the end user, or SA-Open which would show up as an open ticket for the end user.
For the available templates that can be used, this is set in Service Desk under the: Administration tab-> Support Automation-> Service Desk Integration-> Request/Incident Template Associations or Issue template Associations.