There are a few caveats with using these approaches:
1) Toxicity is heavily contextual, not just by topic (as the demo texts indicate), but also by source; at the risk of starting a political debate, a comment that would be considered toxic by the NYT/Guardian (i.e. the sources Google partnered with) may not regarded by toxic on conservative sites. It makes training a model much more difficult, but it's necessary to do so to get an unbiased, heterogenous sample.
2) When looking at comments only, there's a selection bias toward "readable" comments, while anyone who has played online games know that toxic commentary is often less "Your wrong" and more "lol kill urself :D"
3) Neural networks still have difficulty with sarcastic comments and could miscontrue sarcasm as toxic, which users on Hacker News would absolutely never believe.