You seem to want to limit the definition of "aircraft carrier" to STOBAR and CATOBAR ships only, but there isn't a single naval authority in the world who would agree with that definition. An aircraft carrier is a ship outfitted to carry and launch large numbers of aircraft. That's the definition everyone in the world but you uses, and the STVOL/VTOL carrier has been a recognized form of it since the Moskvas and includes some fairly important ships down the years in the Italian, Japanese, Indian, and Spanish navies.
They're not quite as capable as STOBAR ships, but they're more than sufficient to fulfill the traditional roles of carrier-as-fleet-escort: providing ASW aircraft and yeoman CAP. The difference between VSTOL and STOBAR ships in role and even capability is minimal. The real divide in carrier capability is between VSTOL/STOBAR and CATOBAR carriers, as the latter are capable of launching aircraft that are carrying heavy bombloads for strike work and hence can serve the carrier-as-power-projection role.
If you were going to make a "these are not aircraft carriers" argument you chose the worst possible place to put the dividing line.