There is no double or triple voting happening in the same state that I'm aware of.
So I don't think voter ID would do anything to stop this kind of fraud. Assuming the investigation shows it is actually going on.
It will be determined, like it has in the past, a great many of these 765 cases of matches are clerical errors / input mistakes. They very well may find a few. A few.
You also have to consider someone would have to have physical residence in both states, and have the means and motivation to travel to the other state to vote and cast one extra vote that would put them in jeopardy of being charged with a felony, huge fines, and possible jail time.
How many of those with dual residencies would be motivated that much they would risk prison time for the sake of one extra vote?
I submit not too many.