Researcher has developed, at a cost of less than one dollar, a wireless light switch that runs without batteries, can be installed anywhere on a wall and could reduce the cost of wiring a house by …::A U of A engineering researcher has developed a wireless light switch that could reduce the cost of wiring a house by as much as 50 per cent.
No. They need a separate rf field generator. Not just picking up on any stray rf or rf from your wifi. It says as much in the article.
As to the technical reasons behind why your routers frequency can’t be used, I don’t know. I’m guessing the 2.4 and 5ghz range just isn’t something that works at a proper enough frequency to oscillate and gather charge. They’ve been using a lower frequency of around 915 mhz for rf chargers.