Above it says that MSVC2005 is needed for this game but that does not appear to be the case for Anniversary Edition, rather on a brand new Windows 10 64bit installation, Titan Quest Anniversary Edition needs the Microsoft VC2012 Update 4 installer installed manually. Get both the 32bit and 64bit versions as various games will need them.
https://www.microsoft.com/en-us/download/details.aspx?id=30679 Without this the game launch spits out an error about missing msvcp110.dll which I looked into and it does not come with the VC2005 redistributables but the 2012 version instead. GOG support pages for this game should have this fix listed for Windows 10 users, or better yet, since they're "redistributable", why isn't GOG ... you know ... redistributing the libraries the game actually needs to run?
Just an idea. Just throwin' that out there... I'm just saying... :oP
Anyhow, I just helped a friend get this to work over the phone who was going insane because none of the advice on GOG or elsewhere would get the game to work. VC2012 redists fixed it so I thought I should pass it on for the next guy.