Using the default TWebBrowser makes things easy to embed a web browser. Unfortunately the one that comes in by default is IE<n>.
I'm wondering how does one integrate a Gecko or WebKit one.
TWebBrowser is IE. It is not a plugable construction for browsers. You can have other browsers integrated in your application. See
This answer is from '08 and since then time has moved on. The links don't work anymore and there are probably better alternatives now.