The paper you should read to understand how they build that dataset is the following:
At the end of section 2 the authors write:
Finally, like the tests of Fama and French (1998), Griffin (2002),
Hou, Karolyi, and Kho (2011), and others, our tests of international
asset pricing models ignore exchange rate risk. This means we
implicitly assume either (i) complete purchasing power parity
(relative prices of goods are the same everywhere and an exchange rate
is just the ratio of the nominal prices of any good in two countries)
or (ii) the assets we consider cannot be used to hedge exchange risk.
See, e.g., Fama and Farber (1979) and Adler and Dumas (1983), for the
theory, and Dumas and Solnik (1995) and Zhang (2006) for empirical
tests that allow for exchange risk. Exchange risks are thus a
potential problem in our inferences.
I think this answers your question.