Is my device rooted if I can delete system app, but doesn't have SU installed?
In addition to Hussain's answer (whether the existence of SU app tells the device is rooted or not), the fact that you can access /system folder gives a strong indicator that your device is already rooted.

Note that it seems A13 tablets usually come pre-rooted; they are already rooted when out from factory.


  From the little bit I'm seeing of these A13 tablets, [...] , and I can get root, which most people seem to agree that they usually come pre-rooted, [...]


(Emphasis mine)