Magento 2 Checkout post code (zip code) is not a required filed
I found my problem...
Magento 2 has a built in feature that allows the user to specify countries for optional post code.
In that feature, you can remove validation for selected countries.
Settings can be found in: Admin Panel > Stores > Settings > Configuration > General > General > Country options > Zip/Postal Code is Optional for
You have to un-tick the "Use system value" and un-select the countries that you want the post code to be validated for.
I should have properly looked through configurations rather than jumping straight to the code... I hope someone will find this useful.