This isn't an induction, but a LED lightbulb, and I bet that the "Wireless" thing here is a hoax: There is a small battery inside the base of the lamp, supplying voltage to the electronics and the LEDs, and this is what allows the lamp to operate without connecting it to the mains, so there is no any wireless stuff at all.
Take care while posting such product placements. These are often may show unrealistic stuff and big fat lies.
I don't think that it is powered by a battery in the base. There is a video game console around here called "Skylanders" and you put action figures on the pad which makes LED lights in the action figure glow. They have no batteries or anything in them, so this light bulb probably operates on a similar principle.