The reason you're having problems is because the library is not in the root of the repository, and thus not in the root of the .zip file you download from GitHub. The Arduino IDE's Sketch > Include Library > Add .ZIP Library requires this structure. It is also required that when you manually install a library to \documents\Arduino\libraries that the folder you install contains the library in the root, rather than in a subfolder.
This can be a bit confusing because there are actually two different libary formats (the Modbus library is the the "1.0" format), so it's easiest to just let the Arduino IDE install the library for you, and especially easy when the library author has added it to the Arduino Library Manager index (which unfortunately was not done for this Modbus library), but still useful information for when you need to do an update or uninstall of a library.
You can install the library by following these instructions
(In the Arduino IDE) Sketch > Include Library > Add .ZIP Library
From the unzipped folder, select the libraries/Modbus subfolder.
Click the "Open" button.
Despite the menu name, Sketch > Include Library > Add .ZIP Library can actually install from folders as well as .zip files.
Now you have the Modbus library installed, but you might have noticed there were some other folders under the libraries subfolder of the unzipped folder. Each of those folders contains a companion library to the Modbus library. You can see an explanation of the purpose of those libraries here:
If you want to install any of those libraries, just follow the instructions above, but select the folder of the library you want to install instead of libraries/Modbus.