No, the Quicken Medical Expense Manager won't work with Windows 10. According to some data found through Amazon, you can install this application only on Windows NT, Windows 98, Windows 2000, Windows Me, Windows XP. As you can see, there is no Windows 10 version of the product.
Secondly, the Expense Manager is not a valid product anymore. It appears as being unavailable therefore discontinued the product was released back in 2005.