It looks like a simple uninstall and re-install of the rewrite module will do the trick.
Edit: As others have said – try a repair first – if it works then that should be faster.
It doesn’t look like the Microsoft Web Platform Installer is able to uninstall it so just go to Programs and Features to uninstall it.
You’ll find it listed as IIS URL Rewrite Module 2 and just click the Uninstall button on top.
Then reinstall it from here:
http://www.iis.net/downloads/microsoft/url-rewrite
Make sure your App Pool is started – or just restart IIS and it should all work again.
Edit: 8/30/16 : A similar but unrelated error can occur if you have the ‘new’ .NET core installed and update to Win 10 Anniversary edition. See here: https://github.com/aspnet/Home/issues/1583 – Running a repair on VS 2015 Tooling Preview should fix it. Wanted to add it here since the errors are very similar to this answer.