How to submit an article (for example, on arXiv) without being affiliated to any institution?
The text you found tells you that you must not claim some affiliation which you do not actually have. So either leave the affiliation field empty, or enter something like "Independent Researcher".

You will then probably have to go through the endorsement procedure. For that, you need some researchers that have published in the category you are aiming for before to state that they think you should be allowed to publish to the arXiv.