Possibly. A relay type voltage stabilizer generally just uses an autotransformer. One that big, and with the light loading from a laptop, could work at twice the voltage. The unloaded reactance is probably high enough to stop it from overheating at 220V. The size of the transformer looks like it may be rated for 300-500W, your laptop probably draws less than 100W. It could stay out of the danger zone at 220V if you don't load it heavily.
This device will have taps to for a higher or lower voltage output - probably the red, yellow, blue and orange wires, a common connection - probably the black wire, and a low-voltage tap to power the electronics and provide a sense input - probably the white wire.
Adapting it to 220V may be as simple as changing a connection or resistor value on the sense circuit, and possibly the MOV (protection device, the red thing marked "V1" at the lower left of the first picture).
But without a schematic, I'm afraid we will not get very far. Try searching on the name or model number along with the word "schematic" or "circuit".