After installing the needed runtimes I tried to start Titan Quest. The screen went black for a few seconds and the it went back to desktop.
I tried again, but when I click on the desktop icon it says that the target of the link has been "altered or moved" and Windows then deleted the icon.. Then I looked in the TQ directory and the TQ exe was gone! It just disappeared! What the fuck is going on?

I can't tell you what happened but I can offer my suggestions as to what I would do if it happened to me.

If you are running Win 7 or above make sure you have the DirectX End-User Runtimes (June 2010) installed. If you don't know then download and install from this link. https://www.microsoft.com/en-us/download/details.aspx?id=8109 Reinstalling won't hurt anything.

The download will unzip to a directory on C drive. Find the "Setup.exe" and run it as an admin. After install there is no interface or actions required. You can delete the unzip directory after your install.

I would then reinstall Titan Quest to a directory outside of Program Files (xx). I use C:\Games. Make sure to run the install as an admin. When it gets to the C++ install select repair for both. After install is complete, right click the game icon, select Properties, the Compatibility tab and check "Run this program as an administrator". I have reinstalled TQ like this after every "update" download with no problems. All my saves are there as well.

If all your games are installed in a directory located in Program File(xx) and you are not having any problems just reinstall the game in it's current folder location and ignore the advice about installing in C:\Games directory.

That's all I can offer, good luck =)

Edit: If you decided to install in C:\Games rather than the original install directory I would uninstall TQ first. Then do a fresh install in the new location.

BTW, after installing the DirectX End-User Runtimes you don't need to install them again. Once installed you are good to go unless you restore your system to a date prior to the install. I just recommend installing the DirectX End-User Runtimes as so many older games require the runtimes and having them installed eliminates future problems from not having the runtimes. Hard to determine that that is the problem usually.

Check your antivirus. Chances are that is throwing a tantrum and removing the executable for whatever reason. Just whitelist the installation directory for the future.

I agree with Deinmaar. That should have been my first insight when you said the exe disappeared. Sorry for the misdirection.

I checked Avast, and in fact, it did remove the exe. I let Avast restore the exe, but it`s a 0 byte exe now!!

whitelist then reinstall.. should work