Maybe. I don't think it's about the absence of a programming language as such, but more about how you can so easily avoid it. On the old BBC, you more-or-less had to use BASIC. Even if all you started with was
you were still programming. The step from there to writing a simple "Hello World", and then more complicated things, was really small. (And the manual expected you would do, at least a little bit). Then, if you wanted to play more games, there were the listing magazines. Even if you just typed them in without understanding to start with, you'd start to pick little bits up for yourself. And the contents of the magazines were mostly "good but improvable" so "I could do better" was a reachable target.
Nowadays, the step from "double-click to run an application" to "choose language; search internet for programming environment; install environment; enter program" is very very large - and more importantly, you have to decide you want to do it first, and then go through a whole series of steps to get started. And Python, which is probably closest to BBC BASIC in the sense of having a nice interactive interpreter, is not an obvious choice for this unless someone already knowledgeable is deliberately teaching you, and it doesn't come with Windows.
The other nice thing with the BBC is that primitive sprite and line-drawing graphics were very easily accessible. You want to do anything on a modern PC beyond printing a line of plain white text at a time and you'll have to dig into ncurses just to get colourful text - or something like SDL, OpenGL, DirectX, or whatever, if you want actual graphics.
I think "game modification languages" might be the next entry point - rather than reinventions of Basic, or similar, and trying to get back to an environment which doesn't make sense nowadays - they may be limited purpose, but you get instant results, you've got lots of existing code to look at for examples, you can start small and go up to "among the best" quicker than in more general programming, and someone else has already done the work to mess around with libraries, compilers, and the rest.