RX100 portrait - can RX1 do it like this?

That is an error. The perspective is purely a function of your distance to the subject. You won't get shallower depth of field by cropping, and of course you lose resolution, but by standing at the same distance you would stand to shoot with a fifty, and cropping, you will get identical results, albeit deeper DOF for the same aperture, and less resolution, which isn't as critical for most portraits.

As far as lens distortion goes, it corrects well whether in camera (jpegs) or in Lightroom.

All that being said, if you expect to mostly shoot head/shoulders type portraits,look elsewhere.