He qualifies for the title on both grounds:
- He knows elven language
- His ancestors are elf-friends
The strain of elven blood and his choice qualify him as an elf, right, but the source of the narrative of The Hobbit is supposedly Bilbo, who may have not known so much of the history at the time, and had Elrond described by Gandalf, who chose such a description for the sake of simplicity or any other reason
cf numenoreans, who ceased to be elf-friends as soon as they forbade the elven tongue on their isle.