This is explained in the Methodology section of the paper:
We calculate for each head how often it assigns its maximum attention weight (excluding EOS) to a token with which it is in one of the aforementioned dependency relations. We count each relation separately and allow the relation to hold in either direction between the two tokens.
nsubj dependency label is used in arcs between the verb ($v$) and a subject ($s$). In the paper, they define this "dependency score" taking the maximum attention weight and checking if it points to the expected word according to the dependency parse arc, in either of the directions. This is why they count it from verb to subject and from subject to verb.
If you want to know more about the conventions usually followed in dependency parsing, including these
amod, etc, you can take a look at the Stanford typed dependencies manual.