Yes, the software will work on Windows 10, but there won't be any possibility to register it because the registration button from the application leads to another website that has different content and nothing about The Golfer's Diary. You can also install it, but due to the impossibility to register it, the software will expire in 9 days then it will be completely useless.
As an alternative, use ScoreKeeper: http://www.scorekeeper.com/