Chrome Inline Install for extension not working

Your Chrome Web Store item doesn't show the verified site. If you compare it to the "We Heart It" extension, which can be inline installed from http://weheartit.com/heart-button, it has a green check saying "from weheartit.com". You'll need to edit your Web Store item, and associate your verified site with the item.

As of December 2018 (Chrome version 71), Google has disabled this feature. The workaround is to send the user to your extension in the Chrome Web Store.

Source: https://developer.chrome.com/extensions/inline_faq#change_dec18

What will change in M71 (Dec 2018)?

Beginning in M71, Chrome will no longer support the chrome.webstore.install() method and calling it will fail, resulting in a broken installation flow on your site. At this point calls to the API will throw a JavaScript TypeError. You should remove any calls to the API method before this date.