I can't load the YT page, but my guess is they are using the charging circuitry from the camera flash (which uses high voltage, in the 200-300V+ range, often enough) to run the bulb instead of charging the capacitor to discharge across the flash tube.
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Just keep in mind that the circuit usually isn't meant to run continuously, so you'd have to add heatsinks to various parts, or actively cool them in some way, and also remember that Wh is still Wh, and a tiny AA battery won't run a high-wattage bulb very long.