In electronics engineering we often simplify our reasoning for "small signal" analysis where we consider that our circuit has lineair behaviour which means that we can sum signal intensities and therefore also multiply them with fixed values.
The behaviour for a signal of 1V is then similar as the behavior for a signal of 1mV - we just need to divide by 5000.
Sure, there are "non-linear" limitations, one of them being the voltage supply. Therefore, you can not have a signal output of 5000V. However as we know that the output is 5000V for 1V in the "ideal case", then we know that the output is 2.5V for 0.5mV which can be a realistic case.
How is this open-loop gain measured?
First it is determined through simulation. The very small input differential signal can be easily compared to the output signal. So this is some kind of voltage meter, even if it is virtual.
I am sure that there are also practical setups to verify it, but I can't remember them. Sometimes the measurement method is mentionned in the OPAMP specification.
The circuit does not have to be in open loop to determine the open loop gain. The open loop gain is present, even if the loop is closed. We can find the gain of the OPAMP by comparing it's output level with the difference on its inputs.
We also want to know the open loop gain at different frequencies and this is often depicted through the diagrams we find in a Bode plot that depicts the gain with frequency and the phase shift with frequency.
What's the point of the open-loop gain if the actual output voltage can never be that high
As indicated, we consider this in a "ideal" setup and we actually want this to be true for "actual" voltages.
The origin of this word is surely historic. In the beginning of electronics, there were no Printed Circuit Board. In fact, I have some radios where the electronic lamps are interconnected with wires going directly from one point to the other in the 3D space of the radio.
As an improvement, some "rails" were added where the interconnection with the GND (reference voltage) could be made. This was surely also repeated with the regulated power.
My current electrical installation still has rails for the earth, P and N connections.
So the rails represented "ground" and "power". We still continue to call them like this. It's also a pratical way to imagine ground and power as two rails that "limit" the signal or are the boundaries of normal circuit operation. When drawing a schematic we can even start by drawing the ground and power line as horizontal lines and connect our circuit to them as required.