For their CES coverage they said they used MacBooks. They just also brought a Mac mini along that they hooked up to fast internet in a nearby e-sports venue that they used as a backup option to remote into and edit videos from.
They don't, but they do idle as low a 4W for the whole system[1] so running one off a large portable battery would be possible (if not exactly elegant).
You'd need a battery with UPS-like functionality (and doesn't beep when it's taken off power), otherwise every time you plug and unplug it your mac would restart.
Which is surprisingly hard to find for a portable (usb-C) battery.
I assume they meant why is the power interrupted if it switches from charging to not, and I believe the answer is "it's cutting from just vampire tapping the incoming power to feed outgoing, and it would need either chunky capacitors or to be constantly wearing on the battery to not do that".