When searching on Google with IE and Firefox, you are probably not logged in to your Google account. This means that you are searching via the normal HTTP protocol and the plugin can detect the used search terms via the HTTP_REFERER (yes, one R) value.
But when logged in to your Google account in Chrome, you are searching via HTTP with the secure socket layer SSL as you can see by the httpS:// in front of the URL. The fact that your site does not use that same security layer results in that the HTTP_REFERER value gets stripped and the search terms cannot be detected by my plugin…
This is a known issue and multitudes of web marketing companies are pulling their own hair out over it. Getting to know the used search terms is a very valuable asset in determining marketing strategy but since a lot of searches come from logged in Google users, they are missing out on a large chunk of that information.
Although with less impact that that, my plugin suffers from the same problem and, as far as I know, there is no way around it. Except buying a security certificate and hosting your site as https:// but I’m pretty sure that is not worth it ??