My understanding of the solution is a little different. The virtue of the cryptography scheme was that by adding pending characters carefully, it became useless

My understanding of the solution is a little different. The virtue of the cryptography scheme was that by adding pending characters carefully, it became useless to use frequency analysis of single letters. However, what the solution does is look for digraphs - pairs of letters like "th" or "qu" that are common in english. (And, placing low scores to unlikely digraphs like "dx".) Doing two rows at a time is just part of this strategy.