Hmm... It probably has something to do with the fact that the WebKeyboard has been removed from the main distribution package in the later SVN:s
My version of the plugin from that date forward contains its own implementation of the keyboard. So, if you compiled using an SVN from after 13/02/2007, but sources from before that date, the keyboard won't work. If you compiled using MP 0.2.2.0 or SVN before 13/02/2007, but sources from after that date, the keyboard won't work.
I checked out the latest version using svn, but while DialogWebKeyboard.cs is referenced in the project, it isn't in svn - see http://mp-plugins.svn.sourceforge.net/viewvc/mp-plugins/trunk/plugins/WebBrowser/
I tried using a copy from the zip file, but if I build it using the core.dll, dialogs.dll, and utils.dll from 2.2.0 the pop up keyboard doesn't work for me (when used with 2.2.0).
My goal was to get the latest web browser version that is sized properly to work with widescreen skins to work with the current stable 2.2 - except for the keyboard issue it seems to work OK. I wanted to stick with 2.2 since a lot of the other plugins need to be modified/rebuilt to work with the new svn ... six of one half dozen of the other.
I had assumed that since the new svn contains the keyboard code it could be compiled to work with the "older" 2.2, but apparently there is still a mismatch somewhere.