no, you don't need any web server in order to see the demos, because Lightstreamer Server is also a web server, though it offers only basic functionality.
So, you can ask for pages to Lightstreamer Server from your browser. You might get it via a URL of the form "
http://testpc.mycompany.com:8080".
As a web server, Lightstreamer Server supplies the pages it finds under the "pages" subdirectory, where the installed demos (actually, only the StockListDemo) are deployed.
Of course, in a production scenario, you would need a "real" web server in order to supply your pages and Lightstreamer Server would be used as a streaming server only.
This kind of deployment is not covered in GETTING_STARTED.TXT, but it is described in
DOCS-SDKs\sdk_client_web\examples\StockListDemo\README.TXT
as "External deployment".
Dario