You're right. The Draft information for WWI does say 15 Oct 1876.
World War I Draft Registration Cards, 1917-1918
Name: Charles Matthew Cantwell Doran
City: Norfolk
County: Norfolk (Independent City)
State: Virginia
Birth Date: 15 Oct 1876
Race: White
FHL Roll Number: 1984907
DraftBoard: 2

While the 1910 Federal Census says "about" 1877.

The draft record also says he was of "medium" height and "medium" build with blue eyes and slightly bald.
Occupation: Attorney at Law.

So where's the problem?