Assuming that it is a real recording of Wilson, the accent could be explained by his working as a professor and the need to be heard. Frankly, people were better public speakers then. They also spoke for longer.
That is amazing audio quality as you said. Here is another recording of Calvin Coolidge and is message was as relevant then as it is now.
http://www.youtube.com/watch?v=5puwTrLRhmw&feature=related