Anyone of Eurasian ancestry is technically Eurasian. Eurasia is a continent that includes West Eurasia (Europe) and East Eurasia (Asia). It's all one continent though, called Eurasia and it's people are all Eurasians.
The terms European and Asian only came about to be a distinction of west and east of Eurasia. Only uneducated people don't realize it's all one continent, one people.