I've heard the term "dago" quite often throughout my lifetime, and 100% of the time it was used to refer to an Italian-American.
Perhaps it's a regional thing. The entry in Merriam-Webster says:
usually offensive
: a person of Italian or Spanish birth or descent
The Free Dictionary's entry says:
da·go also Da·go (dg)
n. pl. da·gos also Da·gos or da·goes also Da·goes Offensive Slang
Used as a disparaging term for an Italian, Spaniard, or Portuguese.
YourDictionary says:
SLANG a person, often dark-skinned, of Spanish, Portuguese, or, now esp., Italian descent: a term of hostility and contempt
Longman's Dictionary of Contemporary English says:
a very offensive word for someone from Spain, Italy, or Portugal. Do not use this word.