It depends on what you consider "similar", but no, the rotation of the paper has nothing to do with the rotation of helicopter blades during autorotation. In that case, the blades act like ordinary wings and they do an ordinary glide, albeit in a circular direction because the blades are fixed at one end. What happens with the paper is different. The axis of rotation is horizontal rather than vertical.
However, there is a sort of rotation about a horizontal axis in an ordinary wing because a wing produces vortices, and this is a necessary part of the process of producing lift [1]. In heavy aircraft these vortices can be surprisingly powerful and long-lasting, to the point where they can cause smaller aircraft to lose control and even crash if they get caught in one [2].
That first reference has an excellent description of what was going on in my design [3].
It depends on how you interpret the parent comment, but my guess is no. The autorotation you're speaking of happens in a plane roughly parallel to the ground. This is a very powerful and stable way for a wing to generate lift: https://www.av8n.com/how/htm/spins.html#sec-samara
There's another option, which is counter-rotation along an axis parallel to the ground, and orthogonal to the direction of travel. This mechanically induces circulation, which produces lift (by the same principle that a curveball produces sideways lift.) Here's more information on this funky phenomenon: https://www.av8n.com/how/htm/airfoils.html#sec-spinners
Actually in this case he’s using an airfoil spinning on a horizontal axis perpendicular to the direction of flight.
But yes, helicopters can be safely landed this way without power (not crash landed, but actually landed, though crashing is always an option lol)
Also, gyrocopters use the same principle for all phases of controlled flight, by simply using a traction engine to move the aircraft foreword, with a free spinning, unpowered, typically fixed pitch or no cyclic control rotor providing the lift.
When I was trying to get a helicopter license (pre-pandemic), I did one of these as part of training (the instructor had me actually complete the landing... he was a little crazy) and I wouldn't exactly consider it a typical landing, but the helicopter and its occupants were indeed in working order.