I had a similar issue where I was not able to either install a CRX file into Chrome.
It turns out that since I had my Downloads folder set to a network mapped drive, it would not allow Chrome to install any extensions and would either do nothing (drag and drop on Chrome) or ask me to download the extension (if I clicked a link from the Web Store).
Setting the Downloads folder to a local disk directory instead of a network directory allowed extensions to be installed.
Running: 20.0.1132.57 m