After 4 or 5 unsuccessful tries this is how I managed to do it:
System: Win 10 Home 64; No AV, AntiMalware etc. except Windows Defender
1 - Uninstall the previous, unsuccessful install. If you have other office related stuff in the list you see in the "uninstall or change a program" window uninstall them too.
2 - Restart your PC.
3 - Stay online but deactivate "real-time protection" from windows defender settings. (If you have other AV etc. deactivate them too)
4 - Create 3 new folders with random names.
Cut&paste "KMSautonet...exe" file into one of them and rename it, make sure its name doesn't resemble a crack-file's name.
Cut&paste all the read.me files into the second folder you've created.
Cut&paste all the other files into the third folder.
Delete the original folder.
5 - There are 3 different setup.exe files in the folder. Run setup64.exe (AS ADMINISTRATOR) if your system is 64bit .
6 - After the installation ends close the related window.
7 - Open Word by double-clicking on WINWORD.EXE which you can find here: C:\Program Files\Microsoft Office\root\Office16
8 - Just close or accept whatever window opens on Word's splash screen. Don't try to open a document.
9 - Close Word.
10 - Run the KMS activator file AS ADMINISTRATOR whose name you changed .
11 - If a warning pops up that says something like "Convert Office Retail -> VL" choose OK. Choose the related option in the following window that opens automatically; wait couple of seconds.
12 - Now you must see the KMS AutoNET2015 v1.3.8 main window. Click on "Activate Office".
13 - Wait like a minute or so until you see the auto-scrolling log stops. It finishes by a line telling the process was successful.
14 - Now you have to able to open Word without problems.
