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the red thingy on the right side, visible on the third picture looks like a stylus.

Yes, but that appears to be a pic of the "Yoga", not the "Yoga 2", so I'm not sure both new laptops have this ability.

It is a Thinkpad Yoga as it says under the picture: "The ThinkPad Yoga is a bendy laptop that means business". And yes it has a stylus.