You are of course right, but you should have pointed out that the text quoted by you was not 100% wrong, because the ten cathodes have indeed the forms of the ten digits and they are stacked one above the other.

The only wrong parts were that the cathodes are not filaments and the cathodes themselves do not glow.

The Nixie tubes are filled with neon at low pressure and the electric discharges through them produce the so-called negative light, i.e. where the luminescent gas is confined around the cathode. Therefore the negative light takes the shape of the cathode. The cathodes are not glowing, but they are surrounded by glowing neon gas.

In my opinion, negative light, which comes from an apparently empty space, looks somehow more beautiful than solid light emitters, like an incandescent filament or a fluorescent lamp (like VFD, i.e. vacuum fluorescent displays; display tubes with incandescent filaments or with fluorescent segments were alternatives to Nixie tubes, until all of them were replaced by cheaper LEDs and LCDs).

The neon tubes that were used in advertising for making letters or other shapes, use positive light instead of negative light, i.e. where the luminescent gas occupies most of the glass tube, away from the electrodes, so giving various shapes to the glass tube provides various shapes of the visible light, regardless of the shapes of the electrodes (unlike for negative light, where the shape of the cathode matters, while the shape of the glass tube is irrelevant).