The "Interpretation of Article 4" on page 10 of the PDF has nothing to do with aircraft registered in a third country - it is simply pointing out that an EASA licence is not required for Annex II aircraft unless it is a historic or ex-military aircraft or a replica thereof and is being flown for public transport or aerial work.
The only reference that I can find to Article 62 is in paragraph 5, which deals only with the validation of third country licences to fly EASA registered aircraft. There is nothing in the PDF relevant to the requirements for third country aircraft, which is hardly surprising as it will not be Licensing and Training Standards that has to enforce that aspect of the Regulation.