As usual, it looks like their arithmetic is correct, given the assumptions they've made, about the open reading frame being very long for this new gene.
However, I believe that both the original plasmid and the result of the mutation have been sequenced, and the nylon-digesting gene has indeed been found to be the result of a frame-shift mutation from a previously useful gene. I think the way the article keeps trying to deny that a frame-shift mutation could have done this is then dishonest. The best argument they make in that line is that there seems to be an extra mechanism to encourage mutations in that region of the plasmid, which is fairly interesting in its own right.
Also, I don't appreciate their argument that this cannot be considered a "gene duplication --> new gene" event. There can be more than one copy of the plasmid in the cell, so you could easily maintain a mixture of the two probabilistically.
Of course, the real problem with the article is the way it keeps referring to evolution as a process simply based on randomness.
Here's a question: do existing genes have a lower probability of having a frame shift mutation generate a stop codon than would be expected given a random sequence of nucleotides with nominal proportions of A, C, T, and G bases? That's one thing I'd like to know before going any further on the subject of AIG's arithmetic. The otehr thing I'll note is that even a chance on the order of 1 in a trillion is not vanishingly small for a population of many billions of bacteria each with multiple copies of the plasmid.