Is Argothian Elder a Druid?
Rule 108.1 states:


  108.1. Use the Oracle™ card reference when determining a card’s wording. A card’s Oracle text can be found using the Gatherer card database at Gatherer.Wizards.com


This means that the text on Gatherer is correct regardless of what is printed on the card.  This is because older cards have been changed, usually to maintain their functionality while the rules have continued to evolve.

Gatherer lists Argothian Elder's type as "Creature — Elf Druid", so it is a druid. Older cards only had a single creature type, in the Grand Creature Type Update most older cards got updated to the newer   structure used today.