Do all of these still work?

Is Steam obligated to continue to support old games until they no longer exist to support them, or can they stop supporting them at any time?

Depends on what you mean by "still work". If you bought them, you can download and play them. If you mean "Do they work on modern OS", it depends entirely on the game. You also have games that are still being sold but don't properly work on modern OSes without community patches (one example is Max Payne 1).