How is this simple circuit working?
You are basically correct, but it is the base where the voltage rises as the room gets dark. The emitter rises as well but is ~0.65 volt lower.

This means the gain/beta/hFE of the transistor is important as to how sensitive it is. A old transistor with poor gain (10) acts as a load to the photoresistor, thus more darkness is needed to make the LED bright.

Todays GP transistors have a gain of about 100, and a MPSA28 Darlington has a gain of 10,000. R5 looks to be 100K, which is fine for the transistor you have.

With a transistor of a gain of only 10, R5 might be as low as 10K, to supply enough drive current to the base. With the MPSA28 R5 could be 1M ohm. Darlingtons have a Vbe drop of ~1.3 volts.

The photoresistor has a wide dynamic range of resistance, so this is a good circuit to practice with in terms of transistor gain vs. bright/dark room, etc.