I went on the internet and found a quilt like yours and every other row has the double whites. So you did read the pattern correctly, it is just a variation of the Irish Chain you weren't expecting.
When I made a double Irish Chain there were two different blocks and this one just has the one block, so it appears easier - maybe it was, don't know. But it will be pretty the more rows you get together. I don't think you will need the sashing, but it would give you another variation.