It WILL have an effect on the other countries outside EU if they have customers from EU.
Terms of Use and Privacy policy of the site should be changed to reflect the coming implementation of that regulation. Otherwise face risks of being sued and fines are up to 20 million Euros.
https://en.wikipedia.org/wiki/General_Data_Protection_Regulation
From the Wikipedia:
The regulation applies if the data controller (an organisation that collects data from EU residents), or processor (an organisation that processes data on behalf of a data controller like cloud service providers), or the data subject (person) is based in the EU. Under certain circumstances, the regulation also applies to organisations based outside the EU if they collect or process personal data of individuals located inside the EU.
According to the European Commission, "personal data is any information relating to an individual, whether it relates to his or her private, professional or public life. It can be anything from a name, a home address, a photo, an email address, bank details, posts on social networking websites, medical information, or a computer’s IP address."