[efaref]

You also don't need to pay it to own a vehicle. You are allowed to own a vehicle without paying this tax as long as you promise not to drive it on the road (SORN). So by that logic it's not a vehicle tax either.

Also, bicycles are vehicles. So surely they should pay Vehicle Tax as well?

A more accurate name would be the "Using a Motorized Vehicle on the Public Road Tax". Let's abbreviate it by dropping all but the last two words. :)