For a variety of reasons (e.g., multi-collinearity), following this procedure would potentially have you tossing the most important contributors to your model. I would use a different mechanism to evaluate the contributors to your model.

A more classical way to tell if something contributes to your model is by evaluating a model with that value compared with the model without it. How do the AIC (or BIC, or LR, or other metric that you like) of the N plausible models compare?

As an aside, the article's approach to evaluating the "significance" of predictors doesn't account for multiple testing. You have ~10 variables in your model, and your best P value is 0.01, which is essentially 0.1 after accounting for multiple testing (Bonferroni), which is not significant classically.