Doesn't change that it's not a country.
Common military in practice, common currency, common laws, common courts and highest authority, common passport rules, etc.
The EU does not need to be a country for their rules to have impacts on countries. I think this is pretty self explanatory though?
My initial comment doesn't really make sense in this context
Common military in practice, common currency, common laws, common courts and highest authority, common passport rules, etc.