At the time, there was no question about this at all. The Beatles were rock, or rock & roll, or whatever devil music was called.
It was only later, after music turned much harder, that people could make the distinction. By these later standards, some of what they did was pop rather than rock. And that’s not even getting into what Eleanor Rigby or Michelle might be.
There are some contexts in which the distinction makes sense, at least on a song by song basis. If you’re talking about them historically, then it makes little sense to label them as anything but a rock band, since that’s how they were seen for the entirety of their active career. (I don’t remember anybody talking about them as pop, and if that distinction was used in Britain it may not have been an issue in America.) If you want to argue about the difference between rock & roll and rock, you can do that to, and we’ve had a few threads on it (with the consensus being that The Beatles were rock).
John and Paul hoovered in influences from every kind of music present in the 1950s and combined those in an amplified form. It never really made sense to stick a one-word label on a group that changed their sound every year they were in existence, and drove changes in the entire music world at the same time. But the same can be said for “rock” and most of the definitions in the OP are pretty silly, IMO.