Agree. Although it is a hane, and it is "at the head of two", that does not count as a "hane at the head of two" as the term is understood.
It is closer to hane at the head of one and a half, so perhaps it's a "hane at the head of one and three quarters" :-)
I agree with Herman.
In the usual meaning White's stones are getting short on liberties and White could completely reverse the situation by playing hane first herself.
In the example here White's stones have plenty of liberties and it is Black who has some shape issues. In many situations this hane would be an overplay and a one punt jump would be preferred while a true hane at the head of two is allmost allways a good move.