1500W? At 12V that's 125A - That is fucking dangerous! Most sockets are rated at 20A. Most inverters that are >300W use crocodile clips, or preferably screw-down terminal rings. The cable looks way too thin too. That's a fire waiting to happen....
It's ok, that 1500 watt output is only for a microsecond before all the 3 cent "power" MOSFETs inside act as fuses.
More likely, there is enough internal capacitance for the inverter to sustain one (1) half of a full-wave AC cycle at 1500W, after which the overload/low voltage cutout triggers.