I have watched a tutorial about a Magic spiral cube. In the tutorial they are used square paper. It is possible to do the same folding mechanism but use rectangle paper?
Yes, I think you can.
You see how he/she made hexagonal strips but ended up glueing down the triangles?
You could have a rectangle paper that was twice as long as the strip resulted by folding the little triangles down. Or, 3 times as long, or whatever. Then on one end of your long strip you would do it as it was done in the video, and leave the other end loose. Then instead of glueing the next unit on you would just create the next unit from the unused end of the strip.