In it is mentioned that not grounding the oscilloscope is actually workaround if I want to measure grounded circuits but it is not recommended. Didn't get why..
I read that DHO804 is made to run of power bank as well, so I guess it is safe to use it not grounded ?
As per why it is not recommended, as the video explains, if you probe a mains ground-referenced circuit, the probe ground has to be connected to the circuit ground. If you clip your probe on, say, 220V, it will be shorted to ground with very low impedance. That will blow either the circuit, the probe, the oscilloscope or all of them.
On the other hand, if you do that with a floating oscilloscope, the grounding on the probe, the bnc inputs, chassis, etc, will all be at 220V potential with respect to ground, and you might very well be the path of least resistance to earth ground.
Floating the scope allows you to make a differential measurement (only one, all the BNC grounds are at the same potential), as opposed to single-ended with respect to earth ground. I don't think it is worth it, but to each its own. If you find yourself needing that often, look for a differential probe, either used or Micsig.