The study's design cannot address causality. They report a correlation between beta rhythms and the subjects' behavior.
It's unclear whether local field potentials (LFPs), of which "beta rhythms" are one specific frequency band (approximately 12-30hz), are actually a mechanism that the brain uses to transmit information. Information is known to be transmitted via the discharges of single neurons; LFPs represent the aggregate activity of tens of thousands of neurons within ~3mm of a recording electrode. It's possible that these aggregate voltage fluctuations feed back onto the activity of single neurons [0], but LFPs are generally considered an emergent property of populations of neurons as opposed to an information transmission mechanism in their own right.