How is Thief for a player who has only done stealth on recent games like Oblivion and Skyrim? I'd be willing to live without open-world play.

Would I feel like Thief or Thief 2 is missing any important features that those games incorporate? Does Thief have any additional features that make those Single Player RPGs feel lame in the stealth department by comparison?

there is no RPGish character development. apart of that, if you've played Oblivion as a thiefy character, you will probably find many similarities. but, in a way, Thief would be closer to the Splinter Cell series than to Oblivion and similar - closed world, missions, steady story progress, gadgets, weapons (that are meant to be used only in the time of great peril), stealthy infiltration, waiting in the shadows, puzzles, and no skill advancement.

anyway, if you love stealth in any game, the chances that you'll find something you'll like on Thief is pretty good. try out the modernized demos if you want a taste.