I suspect that your outlet has a bad contact, so that (let's hypothesize) one of the prongs does not work. Let's further hypothesize that it's the neutral that has the bad contact.
Also, let us assume that the two neutrals in the outlet are connected to each other. Just not to the power grid.
Suppose that the tester creates a bridge between neutral and ground. The resistance of this bridge is not anywhere near zero ohms, but that might not matter.
What that means is that the neutral receptacles in the socket now have a path to ground, and even if that path is resistive, that completes the circuit. Current can flow from hot, through the device, into the neutral prong (which has no grid connection, but does have a connection to the tester's netural) and then, via the tester, to its ground prong. If the device has a small current draw, then its effective resistance may be significantly greater than the resistance in the tester, and so the tester's resistance might not matter much. The device may see a voltage drop, but its power supply may be tolerant to it.
Anyway, needless to say, replace the outlet.