It may be a conflict with your video card's drivers.
I don't know if you can change drivers with Windows 10 though.
There may be a setting for your video card that helps.
You might try this solution:
Go to AMD Catalyst Control Centre (CCC)
Then go to "Gaming", there should be two main options which are "Gaming Performance" and "Image Quality".
Under "Image Quality" go to "Anti-Aiasing" then change the mode to "Use application settings". Go back to "Image Quality" and click "Anisotropic Filtering" and tick the box next to "Use application settings".
I found the above solution at Steam. It's a fix for invisible characters in a different game but may work.
http://steamcommunity.com/app/241540/discussions/0/864980734722143873/Edit --
I found another thread at Steam where people were having trouble with disappearing character parts in Secret Files 1 and 2.
http://steamcommunity.com/app/40330/discussions/0/613937943015701367/One person said
I have a AMD HD 7800 and I tried an old driver from 2012 and the problem was solved. When I want to update the driver, the problem returns. By now I still haven't found out, where the difference between the older and newer driver is.
So it's a problem with drivers that are "too new."
The original poster described it as "like the game is having issues with the z-order." I had a "disappearing character part" in Grim Fandango where the fix was "turning 32-bit z-buffer off." So maybe something similar could be done in current driver settings related to z-buffer? I haven't found any posts that say this, though I did find posts saying the older Catalyst graphics control center for ATI cards has better controls than the new Crimson control center.