I do enjoy the old 'road tax' semantic argument, or more particularly seeing it vociferously and illogically fumbled.
Of course it's perfectly sensible, acceptable and correct to refer to it as 'road tax' and expect people to understand the term precisely. Car owners only need to pay VED if they use the vehicle on public roads - the emissions angle is a way of scaling it and for the government to influence purchasing decisions in a bid to reduce environmental impact, and you can emit, without paying any emissions penalty, as much as you like in a car on private land if you never use/park it on public roads. So, obviously at least as much a road tax as an emissions tax - i.e. it only applies if you use the vehicle on-road (although one can admittedly argue that exacting an emissions tax is now VED's primary purpose, given that few cars are used exclusively off-road).
And the facts that some other road users are exempt from paying an emissions-scaled or other road tax and that VED revenue isn't ringfenced for road building/maintenance don't mean you can wildly conclude that the VED isn't a deliberate or even de facto road tax, as that is a clear logic failure - even those exempt from paying may have to display a 'free' tax disc when on the road, depending on the type of vehicle, and the free SORN option exists too (the clue is in the name). The fact that fee-payment liability doesn't fall on ALL road users is irrelevant to the semantics and efficacy of terms.
So stop the fallacious and specious argument that 'road tax' doesn't exist, because it quite clearly does for certain types of road user (colloquially and logically, as they are taxed for using the road, not just (and, with a SORN, even) for making emissions), and the OP is quite reasonably asking whether it should be extended to bicycles, which as pointed out by others here it certainly shouldn't for various reasons.