Is this video quality normal (Huawei mate 20 Pro)?

Yesterday I was in a disco and I realize that the video quality diminishes in the dark and I still had 2.5x digital zoom.

Nevertheless, I have heard so much good about the mate 20 pro and have brought me that and I'm not really excited about the quality.

Is this normal or do you think there are any problems?

The chips in smartphones have to be very small, that's just trouble with noise. The noise is especially noticeable in the dark, and possibly even the autofocus has been out of step. Depending on the camera app but you can control it manually, as perhaps more would have been inside. One should not use a digital zoom at all, as one would rather do something afterwards with full resolution in the video cut.

What do you expect at 2.5x digital zoom and bad light? For videos, the camera anyway anyway not as strong as the corresponding Samsung or iPhones in the price range, in photos plays their trump card.

In the price range? So from the reviews on the camera at the mate 20 pro, I've read that nobody currently can beat the smartphone

This is normal, with such a small cell phone sensor you just can't do magic. If the light is low, the sensor will need to raise the ISO and slow down the shutter speed, i. It starts to rush and becomes blurry during movements. If you then re-populate digital zoom, which simply magnifies the pixels, it is clear that the image quality is then rather modest.
If you want to record in the dark you need a camera with a large sensor, so at least Micro Four Thirds.

For photos, right. As far as videos are concerned, iPhone Xs and Note 9 / S9 (+) are better. Under the appropriate conditions, I do not think that they have done much better.