In recent versions of Chrome only CRX3 format is supported:
Instructions for Repackaging
Please see the following article for detailed instructions on how to repackage Chrome apps and extensions into the CRX3 format.
If you use an open source library to build extensions please verify CRX3 support with that vendor. In addition you can use https://crx-checker.appspot.com to check the version of your extension and let your vendor know.
If you are unable to repackage or cannot use the CRX3 format, you can enable the ExtensionAllowInsecureUpdates policy. Note that this is only a temporary workaround, all extensions must move to the CRX3 format!
M76 (July 2019)
By default, CRX2 will be disabled and everyone should move to CRX3.
As a temporary workaround, ExtensionAllowInsecureUpdates can be used to re-enable CRX2.
(from https://www.chromium.org/crx2-deprecation)
Your options are:
Repack the extension in CRX3 format in some way or another, for example with this npm package.
Use one of the other suggested solutions above
In Chrome 75 it seems impossible to add an extension manually. Even if you manage to drag and drop it to chrome://extensions/page – chrome will block it from use.
The only way of distribution now seems to be only through the Chrome Web Store.
https://support.google.com/chrome_webstore/answer/2811969
Also see here: https://github.com/ahwayakchih/crx3#crx_required_proof_missing