Electronic – Grounding balanced secondary isolation transformer for EMI suppression

That's the correct indication for the transformer in its original configuration.

With a normal outlet, the neutral and the ground are bonded together at the service entrance, so the tester will light two lights: one between line and neutral and the other between line and ground, since the same voltage appears across both pairings.

With the tester plugged into the transformer, there's voltage between line and neutral created by the transformer secondary, but now there's no path between your isolated neutral and ground, so now that light on the tester no longer lights, indicating "open ground".

It's not really meaningful to talk about the voltage between two points that are completely isolated from each other. Any attempt to measure the voltage changes it.

Any real-world voltmeter requires a small current to pass in order to measure the voltage, which means it acts like a resistor. For a modern digital meter, this might be about 10MΩ. So by attempting to measure the voltage between two isolated points, you're changing the circuit by connecting them together.

If you actually tried to measure the voltage between A and G, it probably would be about 0V, but only because you've connected them together through the voltmeter. The same goes for B and G. If you connected two voltmeters at once (A to G and B to G), they would probably both read about 115V.