GNSS RTK is incredibly accurate these days. By the time that you're close enough to the landing zone, you're close enough to get positioning down to centimeters on consumer grade hardware, which the article points out.
The actual question is literal: Can SpaceX land a rocket with sub 1 cm (1/2 cm) accuracy? GNSS RTK can get you down to a couple of centimeters, but getting more granular resolution than this isn't reliably possible with current professional grade technologies.
I'm personally unsure if the military has greater resolution than what's possible with RTK or w.r.t. military use GPS, but I would not be surprised if they did. If that's the case, NASA would most likely have access to it, I would assume. But the article specifically calls this out saying that it's not accurate enough to surpass the resolution of using RTK.
What's really cool about these questions is that the same problem space is applicable to self-driving cars and SLAM, if you're into that sort of thing. Lane detection, etc.
Yes, for the purposes of landing speeds. In fact, at vertical aircraft landing speeds, your time-step to position Δ is more accurate than automotive SLAM.
Depends on what you define as 'traditional': basically if you want positioning information via GNSS, the techniques for getting a better reading a fairly well understood, and it doesn't really matter how good your satellites are, the atmospheric distortion is the issue and you need to model and compensate for it by measuring it with a near-enough base station, using multiple frequencies and constellations, and if you're moving, an IMU to constrain your motion over as long a period as you can to effectively average out the other noise sources. Half a centimeter, given all of the above, is better than what I've seen quoted in the space, but not utterly crazily so.
