That's probably the optimal strategy. I'm skeptical of first-principles learning. It's great to immerse yourself in theory, but when you've gone all the way to "topology" you've probably gone beyond the limit of what most ML devs care about on a day-to-day basis.
It's still useful to know. I've applied lots of ideas from other fields. But can you force that knowledge by forcing yourself to study other fields? Maybe. We all have a finite amount of time though.
That said, lots of items on this list are key, and it'd be worth ranking them. There's no need to memorize formulas for Adam, but knowing the concept of momentum-per-weight is pretty crucial.