Be aware that ReplayKit.exe must not be moved after installation, otherwise opening replays will fail.
NOTE: When you have to move it later on it's no big deal though, just run the installation again.
Make sure that you placed the ReplayKitPatch.mpq in your Warcraft III Folder.
Run ReplayKit.exe and accept the permission request. Administrator rights are necessary to connect Warcraft III Replays with this software and to perform the patching later on. Details here. If a "Couldn't synchronize" error occures go here.
Click Yes to install the program.
Now there should pop up a message that the installation succeeded.
If not, make sure that you followed all the steps of this guide. Does this not solve the problem, feel free to contact me :)
NOTE: Don't delete ReplayKit.exe after installation! It's setup and installed software at once, you will still need it.
From now on watch replays via opening the w3g-files. If you open them manually in Warcraft III with help of the View Replays function this software gets bypassed and has no effect!
NOTE: Openening w3g-files means double clicking them or rightlick->open