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Because in 1861 there wasn't much call for motoring laws. Thankfully cycling related offences are so few they don't warrant their own act of Parliament so prosecutors have to fit the offence in with this one.
Hefty-
Both charges are "driving" but the one he is charged with is very loaded that his method was out and out wrong, the driving specific ones are "accidents" and so more lenient.
If you read the wording it's just as true for any death casused by a driver.
Drivers of carriages injuring persons by furious driving.
Whosoever, having the charge of any carriage or vehicle, shall by wanton or furious driving or racing, or other wilful misconduct, or by wilful neglect, do or cause to be done any bodily harm to any person whatsoever, shall be guilty of a misdemeanor, and being convicted thereof shall be liable, at the discretion of the court, to be imprisoned for any term not exceeding two years
Clockwise
What they are being charged from/with.
http://www.legislation.gov.uk/ukpga/Vict/24-25/100/contents
What death by other roadusers is charged from/with.
http://www.legislation.gov.uk/ukpga/1988/52/contents
Just take a look at the other charges in that list, a driver is grouped with those who have a brake light out or other small motoring offences while the cyclist is being grouped with "murder" "child stealing" "shooting" "threats to kill" the list goes on and on.