The endpoint tells you the stage that failure occurred at and the type of failure. i.e. the failureStep and type elements. It's enough to know where things go wrong, for detail I'd look at the UI.
[
{
"ssidNumber": 1,
"vlan": 100,
"clientMac": "22:33:44:55:66:77",
"serial": "Q234-ABCD-5678",
"failureStep": "dns",
"type": "802.1X auth fail",
"ts": "2018-02-11T00:00:00.090210Z"
}
]
Looks like the Connection Log is also pulling data from network events... https://developer.cisco.com/meraki/api-v1/get-network-events/
If you want that info, you'll need to get the events and correlate the two, and maybe data from other endpoints as well.
The UI/API are two different views of underlying datasets, trying to replicate the UI view from the API can be complex or impossible, especially as neither the datasets nor the UI's algorithms and parameters are public.