Yeah, but that doesn't stop other types from thinking visually as well.
Anyone can think visually, just as anyone can do rigorous calculations in one's head.
The difference, I think, for Ni doms and especially INTJs is the Ni is rather reliant upon visual conceptualization to do the calculations, and, moreover, to make sure that whatever calculations are done fit correctly into the overall picture.
I've noticed that one way to spot an Ni dom is that they're good at "word problems". In other words, if it's a problem that is phrased in normal terms but must be transcribed into math or computer code to be solved, Ni doms appear to have a talent for taking the problem, transforming into its more analytical format, solve it, and then transcribe the answer back into normal human language. This jibes very closely with Nardi's observation that Ni doms' "zen state works best when focusing on a single question," developing a holistic model of a problem and then solving it. Personally, I feel a bit crippled if I'm forced into a situation where I have to solve a problem that is simply a puzzle, solved without context, which means I cannot apply my holistic approach. (This mostly happens in interviews where the interviewers present coding puzzles and the like.) Not that I cannot do it, but I essentially have to form my own contrived context(s) before I can move the problem around inside my head and explore possible solutions.
When I'm solving a database architecture problem, for example, I think in terms of what the database is used for (it can be multiple uses, I just need to be aware of them), and then I come up with the simplest design that satisfies those needs and is flexible enough to meet changing needs. I see the data flowing in and out, I can feel where externalities might choke the data flow, I can see how bad data can be accidentally inserted/extracted - it's just there, without any "math", without any specific categories of design patterns or the like (I learned the definition/distinction of OLTP vs OLAP after I had designed databases with those principles - I just didn't have the words.) If I find a bug/problem in the database, I don't just go in and fix that one thing so it's logically self-consistent and fits with what's around it, I make sure that the fix preserves that overall data flow and purpose. This is all mostly visual and holistic, and I mostly tend to use more analytical skills (Te) to ensure that the instantiation of my vision is correct.