According to the article, the tape has to be peeled in a vacuum to get the X-rays. This makes intuitive sense to me; at normal pressures air would ionize and bleed off the electric charge before the charge difference between the just-separated layers of tape reached the tens of thousands of volts needed to create X-rays.
It sounds ingenious as a means of getting X-rays in an environment that has no electricity, but I feel doubtful that it's the most economical way. It would have to be pre-sealed in a vacuum chamber, either spring-powered or cranked through an airtight bearing, meaning it would not be nearly as economical as a mere roll of Scotch tape. Could not a more conventional static electricity source (such as a hand cranked Wimshurst machine) in combination with a common vacuum tube such as the 1B3 found in millions of discarded old TV hulks, be put to the same service? (The tube does not need filament power for this.)