The .NET update has fixed it. Thanks a lot!
I think my PC's updating isn't set up right so I'll fix that!

Thanks again!

--Issue Resolved--

I have two errors appear when I launch the linked launcher. I have linked copy + pastes of the errors from the Steam Launcher and the link Launcher below.

http://pastebin.com/srfsEMWp

A friend of mine has looked over the error logs and believes it's something Visual C++ 2010 related. I believe these problems started AFTER attempting to install PlayWith6. I have tried reinstalling Visual C++ 2010 but as I have newer versions installed, it won't allow me to install it.
PlayWith6 also fails to load and doesn't install correctly.

Sorry for the delay in reply; I forgot that I was going away.

I have extracted the file to the desktop (The file both directly on the desktop and in the folder it arrived in.)

Running the program normally / as admin seems to be doing anything. Nothing opens, my Steam doesn't switch to "In-Game Arma 3", and a error report is not created.

I reinstalled .NET Framework 4.5.2. I then deleted arma3launcher.exe and the Launcher folder.

33 files were reacquired after verification of game cache. Returns same error.
New .txt named:

"After Fix Attempt Arma3Launcher_Exception_20150719T150716.txt"