Most NAND flash use floating gate-mosfets (a type of transistor), which work by storing a very small amount of electricity within a high resistance material to prevent dissipation when in the "on-state". But this charge is extremely negligible in terms of mass, and energy. And depending on the particular memory used, the "off-state" could carry a charge as well.
Interesting to think about though.
(and to clarify, this energy is coming from the device's battery, not the RF energy or something else OTA)
What they're saying is that the electrons captured to change the state in a solid-state drive holds physical mass. If this mass change is extrapolated to the data storage of the entire internet, then it physically ways as much as a strawberry.
This likely means that all recorded data in human history would weigh less than your standard package of printer paper from Staples.