The idea of the article is that certain visualizations can help think through certain problems. Maybe you can hold these visualizations in your head, or maybe you can't (because your aphantasic, they're too complex, you're tired, whatever), but they're just as available to you on paper or in diagramming tools if you need them. It's trying to start a discussion about what helpful visualizations people turn to in specific problem contexts.
It's separately interesting to hear people try to characterize what they visualize in some generic/universal way, but I think it's causing a lot of people to self-diagnose as aphantasic when it's not indicated. You're not obliged to have some vague generalized visualization going on in your head when programming any more than you would be when speaking, or writing, or playing music. More commonly, one might draw on specific visualizations here and there as they enrich and relate to what you're expressing in your art.