The idea here is to harvest the energy from the "RF" ambiant noise, not from a pre-provided relatively powerful signal like the one that is powering RFID tags.
Based on what says the article, the power level of the "ambient" energy is too low to be harversted by current technology except the one presented in this article.
https://e-peas.com/product/aem30940/
https://www.nxp.com/docs/en/application-note/AN12365.pdf
https://www.nexperia.com/products/analog-logic-ics/power-ics...
Also, crystal radios are really old.
For nexperia, if you read the datasheet in fact it is a module that will harvest energy from a photovoltaic cells.
For the e-peas, this is what says the datasheet: "RF input power from -18.5 dBm up to 10 dBm (typical)". So this is just the typical energy harvesting from an incoming signal.
In the original article, they said that their new technology allows to harvest energy under -20 dBm that was impossible till then.