Yup. It doesn't take much to make an SMT LED shine - just a milliamp or two, and an interesting property of that kind of inductive coupling is that, up to a limit, you can couple a higher voltage out of a given signal by increasing the number of turns in your winding. And if you couple out more than the forward voltage of your LED junctions, you can convert the surplus into enough current to visibly light the LEDs as they conduct. So with the right kind of boost circuit - in this application probably just an inductor, although I could be wrong here, analog isn't my forte - driving the LEDs, and a bare-die CMOS shift register that sips a few microamperes for the animation, you can pretty easily produce the kinds of effects I remember seeing back in the before time too - and still miss to this day!
RFID works by the same principle, incidentally - in this case, the energizing signal comes
from a primary winding in the reader housing, and the secondary in the card powers a little CMOS chip that in cheaper models just modulates the voltage drop over the winding to return a constant code, and in more expensive models receives a challenge nonce signaled by the card reader and modulates the winding to return an encrypted response. It's a really interesting application, and an impressive but often overlooked early example of "IoT" style smarts done well.