This seems to be the functional crux of the argument, but it's flawed, for at least a couple reasons.
(1) It presupposes a background in CS and software engineering, as well as knowledge of the ecosystem of tools available online. At some point in your life, you have to have had the time and stability in life to learn all that, and you need time and stability to work towards your goals in the present using those tools.
(2) It's too narrow in scope. This is shown as one example of a general philosophical mindset, but in fact software engineering is uniquely suited to starting out from nothing in this way. You'd be hard-pressed to find analogous examples that require any interaction with the physical environment.
If you're already into software, and you want to learn more about it or build something new, you're right that we have a lot of free resources available online to do so. And I agree that it's good to structure your life, when you can, so that pursuit of wealth isn't important, and you just happen to do so along the way. But I think it's difficult to translate that into a more general point about simply adopting a different outlook on your circumstances to effect meaningful change. There are big swaths of the human experience that that philosophy doesn't speak to.
Second, by bringing up free computer access at a library, it connects the point you're trying to make with the really complicated nuances around poverty. Even assuming we ignore smartphones and tablets (because how can you get any work done on one?), the demographic that only has access to a device with a keyboard at a public library is going to be almost entirely facing (at least) moderate poverty, and life in poverty just looks very different from the kinds of backgrounds that the rest of your piece implicitly addresses. So, you could focus instead on the wealth of free software tools available to the people who are in some range of circumstances to take advantage of them, assuming that access to a device with a keyboard isn't the primary challenge.
I would point out that you'd also have to start, prior to a background in CS and software engineering, with an environment that is stress-free enough to learn/do programming. We know that stress reduces the ability to learn and think rationally, and also that poverty is extremely stressful.
Instead, I think it's basically ok to say that your point applies to people who have reached a certain threshold of stability and security in your life, and isn't meant to imply that people who haven't reached that threshold ought to be able to simply will themselves into doing the same thing.
Were you wearing clothes? What would the librarian's response have been if a naked person walked up and asked to use the computer? Had you showered or bathed recently? What would the librarian's response have been if smelled of body odor? Was your stomach full while you were learning Github and Heroku? How much could you have learned if you were constantly racked by hunger pangs.
Yes, there are ways if you have some money to make it go farther and learn new skills relatively cheaply. However, to say that this is an illustration of wealth irrelevance is really pushing it.
I know this in part because I'm a middle-class CS prof whose stuff is all "on the internet". At one point I had the great idea that I don't need to carry around a laptop, since my stuff is all on the internet anyway. I'll just use public libraries, or other university libraries, problem solved. Sometimes it works, but there are obstacles strewn all about. On a side note, it's also made me appreciate physical books in libraries more. If you really did want to learn something and had $0 to spend, and you can find a physical book on the shelf of a public library, you can read it for as long as the library is open, without a card or 15-minute time limit.
(Edit: I realize the original post was going for something more philosophical, and I see they commented in a sibling comment that they're sorry if they came across as tone deaf. I don't mean to pile on! But wanted to point out that just the bare practical aspect can surprisingly difficult even if you know what you're doing.)
Someone in a minimum wage job would possibly be trying to work overtime or a second job in order to make ends meet, and would have very little time/energy left over to do anything, let alone figure out how to break into the world of software development. Even considering a happy path where someone works ~40 hours/week, has a short commute, and doesn't have dependents to care for, it can still be incredibly challenging to muster the focus necessary to self-tech programming.
I understand that the resources to become successful at software development are freely available, but this post glosses over all the prerequisites (as pointed out by some other comments): ample free time (for years), a growth mindset, intelligence, resourcefulness, etc. If somebody already possesses all those things, then the idea that they can teach themselves valuable skills online would be helpful (if not obvious).
As you said, somebody couldn't accomplish this goal starting from literally "nothing". It might be helpful to identify and delineate what _is_ required to embark on such a journey. That way people who tick a lot of the boxes will feel empowered, and those that don't will have an idea of what it takes to get there.
I think you might be overestimating how many people are self-starters like you.
The pursuit of wealth taints the things you enjoy. All of a sudden all your ideas are qualified and restricted to what can make money. Now instead of building the things you love and enjoy you are building things you think can make a quick buck.