So equipped Atari requires probably more amps than your powerbank can deliver. Or probably not the powerbank itself but the cable, that is very thin and limits the current.
->link<- ^^^ Here you can find some info how to make an Atari USB power cable. Additionally, there is also some information about the power consumption of specific configurations: Quote Atari 65XE fabryczne 560 mA Atari 130XE fabryczne 620 mA Atari 800XL fabryczne 810 mA Atari 800XL + Stereo + Ultimate 830 mA Atari 800XL + Stereo + Ultimate + Side2 + mysz 1000 mA Unquote
From (my) experience, in most cases a 5V/2.2A power supply is more than enough to power an Atari with an additional memory module + Cartrigde or FujiNet or other SIO2SD.
In my opinion, the cable (may be) is to long. The voltage drops with every additional meter of wires... and in the video i can see a "nice cable extension" :) Check the voltage on Atari board (power connection). Should be 5V.
Just to check - I took my full-featured 800XL machine (with U1MB, VBXE, Rapidus and stereo, Side2) and connected it with a USB cable to a stand alone USB HUB (with separate power supply). The machine booted but I noticed that when everything was on (including Rapidus), the power meter reported 1.25A@5V but there were problems with reading a CF card - something similar to your case. But the PSU was not able to deliver more juice, it seemed to have a ~6W power limit. So I took a stand-alone charger with up to 2.4A output. With it connected, the power meter reported up to 1.37A usage at peek (so it's not supprising that 1.25A was not enough) and everything worked just fine.
The power cable I used was built of an old USB cord for a Kindle by Amazon - a really solid piece of wire. I think it's able to deliver a lot of current. And I think, your cable isn't, this is why you're experiencing problems...
