There are directions there for printing and mailing the request form.
I would be sure and include the note that you are searching for genealogical information and to request that you get a copy of the application portion, which would include the information about the bride's and groom's date and place of birth, their parents' names including mother's maiden, etc.
Do you know when Alpheus and/or Hattie were born? There are some online family trees at Ancestry.com that show them both born about 1867. Did Hattie remarry after his death?