The goal is the ability to generate strings that match the "approximate sense of complexity" (ASC) of the subjects. To do so requires the ability to avoid any routine and inhibit prepotent responses.
Research goal was to measure cognitive ability and randomness is just measure stick. The actual mathematical complexity is correlated but there is human bias. The bias itself is irrelevant if it's constant. The relevant is how closely subjects can generate strings that appear random and complex (randomness with bias) for humans.
In other words
measure = statistical randomness + bias
Because the bias is almost universal (see the modulating factors in the article) it's not interfering with the thing they try to measure.
Research goal was to measure cognitive ability and randomness is just measure stick. The actual mathematical complexity is correlated but there is human bias. The bias itself is irrelevant if it's constant. The relevant is how closely subjects can generate strings that appear random and complex (randomness with bias) for humans.
In other words
measure = statistical randomness + bias
Because the bias is almost universal (see the modulating factors in the article) it's not interfering with the thing they try to measure.