Have you looked into "simulation theory"? I'm sure it's not a new idea, but Elon Musk recently helped nudge it into popular philosophy. What I've read on this theory/idea seems to be very similar to what you're pondering here. I myself only have a tenuous grasp on this idea so I fear attempting to explain it, but I will share an experience/thought of my own that will hopefully expand on yours.

I recently played a videogame where you - the main character - become aware of your role as a free agent in a simulated reality (this premise falls somewhere between simulation theory and solipsism - the idea that only one's mind is sure to exist). In this videogame the player experiences a digital universe structured and governed by the same/similar physical and ideological laws we experience here in our own physical universe. After playing through the game's story it is discovered that this simulation has existed for an unfathomable span of time. Once an individual, or agent, becomes "self aware", they are free to do whatever they like; i.e. create a simulation of their experienced reality. Thus the cycle repeats like a mirror's reflection of a mirror. An infinite loop stuck inside the game. But, it is possible to take this a step further, or back, really. If inside this game there are simulations of practical realities repeating one after another, it could be argued that the player his/herself is just one link in a long chain of repeating simulations. If this videogame is simply a phenomenological simulation of our experienced reality, it is possible that what we know as our existence is also, in turn, another entities simulation.

If this argument is true, then your statement about non interactive computer programs is true. The really interesting question would then be: who or what created this theoretic existence?