Browser games are trivial to code. They did not reverse engineer it, they just wrote the same game from scratch.
"multi-million dollar game developments" are you sure we are talking about browser games? You can order a custom game (only code, no art assets) of this kind for 50-70k USD.

Add value. Release new, minor version updates relatively frequently. A rolling target is hard to match, particularly if your updates contain new features or content that people want. Virtual worlds thrive on the size of their population, these private servers will probably be inconsequential if you can keep the bulk of the players moving with you. You can even try to build in game mechanics that only work with large populations, though you could compromise your overall design by over-indulging this. Make the server contain as much of the logic as possible, which means less can be reverse engineered and would need to be written from scratch.

You can make it hard for third party client/servers to be developed by detecting and rejecting protocol errors. You might randomly delay the disconnect for some number of seconds after the protocol error so the developer cannot reliably link the last message sent to the disconnect. You would have to be careful about things like this as they could impact regular users if you ever release a buggy version yourself.

You can make it more difficult through client obfuscation and protocol encryption, but at some level the client will generate something in memory that a determined adversary can read and interpret before it gets encrypted. You cannot prevent it, but you can discourage it, make it hard to do and marginalise those who choose to play on private servers. Finally, you can take legal action against any private community hosters if they start getting to a significant size. Ensure your EULA contains whatever clauses your lawyer believes necessary so you can legally act against such communities if you want to.

If you want to reverse engeneer such game you don't need any "packet sniffers" because to make such a game from scratch you don't even need to know what a packet is The most sophisticated thing you would ever need might be AJAX, and that's it...

I don't know, maybe they indeed had stolen their server code. But I wonder what for? How long would it take for a lone programmer to code something like Habbo Hotel (apart from gfx assets and assuming single server architecture only and ignoring code optimization). A month? Two?
Assume you could obscufate the code of your game perfectly and secure your server against hacking perfectly. Would it make any difference? How many clones of Travian or Ogame are there already? Hundreds?

The key problem is gfx, you can't easily create it from scratch. But also it is impossible to prevent the theft of it...