The farm has not UPA service deployed and I wouldn't do it.
Is it possible to retrieve using JSOM or REST one of the properties that we see in the
_layouts/15/userdisp.aspx? page for a specific user?
I don't find any documentation about getting the user information (no user profile) using JSOM.
I thought I could be able to access these properties using REST (http://sympmarc.com/2014/01/21/getting-user-information-with-the-sharepoint-2013-rest-api/) but I get null for the Department property even if the property is set for the specified user.
As suggested by the @harryB's answer, there is endpoint
siteuserinfolist, however with this REST call I still get a null value for department:
`<d:Department m:null="true" />`