That's correct (although not directly related to the technique): Your eyes always move a little bit, so when we say that "you don't move your eyes" here we simply mean that you don't make large eye movements to look at the letters. But your eyes are always jittering (around a dot center of the display in our case), making tiny movements called 'drift' and 'microsaccades'. Without these small eye movements, vision for things that don't move themselves disappears. I know this only from the literature--it must be quite fascinating to experience this yourself.

Well it's actually very reliable and cheap: The eye tracker used for the video is €100, and selection accuracy (even for naive participants) is over 90%. It's slow though.