RX100 portrait - can RX1 do it like this?

Yes, you can make great portraits with a 35mm equivalent focal length. BUT compared to a longer lens, the results usually won't be as pleasing if you want a more natural look. And if you're shooting portraits or beauty for paid clients, the clients will probably prefer something more realistic / pleasing to the eyes.

Steve Mccurry makes wonderful portraits. But they're mostly photojournalism / environmental portraits which a wider focal length is great for.

It really depends on the taste of the photographer / client, photography genre, and the level of scrutiny the reviewers will put the images through.

For what Steve Mccurry is doing, I couldn't really ask or expect anything better. For the OP and his sample image, I'd definitely want a long lens around 100mm on a tripod. Not a photograph shot with a wide lens that's been cropped to death. Two different types of portraits between the OP and Mccurry which imo require a different type of lens between the two.

Watch this "How Lens Focal Length Shapes the Face & Controls Perspective"

http://www.youtube.com/watch?feature=player_embedded&v=ZRoqNx9rlVA