This might be what you are looking for: http://www.chesslive.de/

This website contains a very good database with all the features (including the no-download) which you mentioned. Unfortunately ChessBase have stopped updating it, but it remains a useful source if you aren't at the level where you need Mega Database or similar products.

Also, when publishing a database online, I recommend you check your database very carefully for doubles - I recall some sites which claim 5 million game databases, but several of these games are doubles or incomplete.

The link you present is a very good example. Chesslab apparently uses a software to handle their database. You can search games there but can not download their database or download a single game from their database.
I am looking for a similar software. I want to publish my database online where people can visit and search games but I do not want those people to download the games of the database or the database itself.

C'mon guys, I posted this message long ago and still there is no answer. There should be some software that lets you do what I dream of. Or maybe there is simply none huh ?
If someone knows such software please let me know.