The use of the word 'carriage' is a good one
Because it's not too specific and can be extended to other forms of wheeled transport without requiring the text of the law to be rewritten. It's left to the courts to decide if a mode of transport is a carriage or not. If only more law was written like this (but then I'd prefer Roman Law anyway rather than our system, but that's getting me started...)
There's a similar case; Corkery v Carpenter (1950), where a man was found guilty of being drunk in charge of a 'carriage' under the Licensing Act of 1872. The court ruled (and it has been subsequently upheld) that bicycles constitute carriages, so I don't think there's much hope of this case deciding otherwise.