According to the article, they can vote, in theory.
I see the issue is that being overseas, the ability to defraud is high. Imagine the “get out the vote for Hilary” cash that overseas Ohio voters could be paid.
They can vote “in theory”, but probably not. U.S. Citizens of Puerto Rico, the US Vigin Islands, Guam, and other territories do not vote. Only citizens resident in the States and DC can vote. So, an overseas citizen would either have to maintain a residence or have recent ties to a State. I think a lot of these overseas citizens have their citizenship by accident or because their parents were citizens, but have not lived in the US. They should not be able to vote.