"Furious" in the 1860s would be more likely to refer to a state of mind. The link for that word to include "speed" may have come along rather later in history.
This intrigued me as its use to mean energetic, wild or violent as in "fast and furious" was I thought established, if not archaic - and Google has revealed that Rabbie Burns used the expression in "Tam O'Shanter" in 1793 in the line -
"The mirth and fun grew fast and furious"
So I think it clear means recklessly fast. And I expect that the endorphin rush of the offending cyclists is the same as those of the dancers responding to the piper's music in Burns' poem.