R-squared isn't what makes it significant. He's saying it's statistically significant (low p-value) and also practically significant (high R-squared). Statistical significance is certainty that there's a pattern; R-square is the strength of the pattern. It's a range from 0 to 1 where the value represents the amount of variation in the dependent variable that's explained by the variation in the independent variable.

20% of all the variation in premature death in developed countries is explained by this one variable, without controlling for anything else. That's enormously significant.