I thought this was an interesting question... although I definitely get the feeling like I'm missing some of the context behind this "planetary boundaries" write-up.
(What is the Stockholm Resilience Center? What are its motives and methods? Why was it doing this analysis, and how did you end up running into it?)
I agree that fertilizer runoff gets talked about a lot less than climate change, and I'm not entirely sure of why that is. I just looked it up, and "Organic"-labeled things apparently do already mandate organic fertilizers (which should be N-neutral on net?). So there's at least that.
Regarding their assessment... one of the factors that seemed to be weighted a lot in their assessment was "level of antropogenic change vs natural variation in Process X." I'd expect that to have heavily-weighted the Nitrogen Cycle, since our interference in it dwarves the variability due to natural processes (something they themselves spell out. The Haber process is a strange, powerful, magical, inorganic thing the humans cooked up).
This metric is... not precisely the same as "level of damage this change can cause." They seem to have set up some sort of threshold for what they consider "dangerously high", and I don't really understand the thought-process or reasoning they used in picking those thresholds. But I think they factored "change vs natural variation" into their thinking a good deal.
My understanding from my own Ag background is that fertilizer runoff really can be a big problem; nitrogen and phosphorus are a major limiting nutrient for plant-life, both on land and in freshwater ecosystems (the ocean surface is iron-limited, interestingly). In a sense, this is exactly why we use it; we want our food crops to grow at a wild rate, one rarely seen in nature.
When there's a sudden influx of nitrogen into a freshwater system, one of the possible consequences is an algal bloom. These go through a boom-and-bust cycle (with the seasons, or resource-availability patterns), leading to a massive algal die-off. During this die-off, decay bacteria wipe out the underwater oxygen-supply, leading to knock-on effects on freshwater ecosystems like massive fish die-offs. Enclosed spaces like lakes are perhaps especially vulnerable, since there is no way for the N and P to ever exit the system, potentially perpetuating the cycle indefinitely.
That said, suddenly cutting fertilizer usage would practically ensure that food production would suddenly drop way down, and that would ill-serve a lot of other human values. Reducing runoff looks like a very hard problem, to me. Finding ways to remove excess P and N from environment seemed to be an area with at least a little bit of interest, but it doesn't seem very actionable on an individual rather than city or state level, which might explain the low publicity? Unsure.