Very annoyingly they never explain what that LED is in the center. Not a peep that I could find. Maybe it shows ground-fault current as 5mA will light a LED just fine. That would show a glow when pressed but since a functioning GFI outlet would trip instantly extinguishing it. You would only see that LED on if the GFI didn't correctly trip. Hmmm.
Over here there are more expensive items that test RCD or RCBO circuits (what the exact differences are between RCD / RCBO and GFCI I'm not sure) but they display the trip current and trip time, as ours generally have a set do not exceed leakage current (i.e. 10mA for hospitals, 30mA general). These devices are usually battery powered and have a standard plug that can be used to connect to the circuit under test.
They're generally safe enough for non-technical people to use them as well.