The example in the article talks about distributing profits/salary. VAT is charged on sales to consumers in the EU. Sales to any EU company with a VAT number is VAT free (reverse charge mechanism), and sales to any person or entity outside the EU is also VAT free.
For sales to individuals in the EU you will have to charge either Estonian VAT (20%—among the lowest in the EU) or the customer’s local VAT rate (depending on what you are selling).
Also non-EU companies are supposed to charge VAT to individuals in the EU, although not all companies follow the rules.
Note that the VAT registration threshold in Estonia is €40,000, meaning that if you have a lower turnover than this per year you don’t have to register or charge VAT to your customers.