Here is the complete archive file. Extract the archive file and move the WhatsApp Web-linux-x64 folder to any folder inside your home folder or directly in your home folder (your preference). I created an Applications folder inside my home folder. Take note of the path to the folder.
Open up the WhatsApp Web.desktop file and change the path for
Exec to match the path of the folder you just moved. Leave "WhatsApp Web" at the end, this marks the name of the executable inside the WhatsApp Web-linux-x64 folder. Now move the WhatsApp Web.desktop file to the following directory: /home/youruser/.local/share/applications. Move the icon from the extracted archive folder to /home/youruser/.local/share/icons.
You should now be able to see "WhatsApp Web" when you start typing 'whatsapp' in Launcher.
Let me know if this works for you.