I'm not sure why you want to assess % deviance since you're not testing analysis of deviance. You are testing variance so you could look at % variance and that's farther up in the tutorial where the R-squared values are reported. You look at the model for the quantity and the test for whether it's significant. The difference in R-squared between the models is the extra amount of variability explained.

Look at % variance farther up in the tutorial where the R-squared values are reported. You look at the model for the quantity of variance explained and the test (anova) for whether the increase across model complexity is significant.